Vincent Selhorst-Jones

Electric Force & Charge

Slide Duration:

Section 1: Motion
Math Review

16m 49s

Intro
0:00
The Metric System
0:26
Distance, Mass, Volume, and Time
0:27
Scientific Notation
1:40
Examples: 47,000,000,000 and 0.00000002
1:41
Significant Figures
3:18
Significant Figures Overview
3:19
Properties of Significant Figures
4:04
How Significant Figures Interact
7:00
Trigonometry Review
8:57
Pythagorean Theorem, sine, cosine, and tangent
8:58
Inverse Trigonometric Functions
9:48
Inverse Trigonometric Functions
9:49
Vectors
10:44
Vectors
10:45
Scalars
12:10
Scalars
12:11
Breaking a Vector into Components
13:17
Breaking a Vector into Components
13:18
Length of a Vector
13:58
Length of a Vector
13:59
Relationship Between Length, Angle, and Coordinates
14:45
One Dimensional Kinematics

26m 2s

Intro
0:00
Position
0:06
Definition and Example of Position
0:07
Distance
1:11
Definition and Example of Distance
1:12
Displacement
1:34
Definition and Example of Displacement
1:35
Comparison
2:45
Distance vs. Displacement
2:46
Notation
2:54
Notation for Location, Distance, and Displacement
2:55
Speed
3:32
Definition and Formula for Speed
3:33
Example: Speed
3:51
Velocity
4:23
Definition and Formula for Velocity
4:24
∆ - Greek: 'Delta'
5:01
∆ or 'Change In'
5:02
Acceleration
6:02
Definition and Formula for Acceleration
6:03
Example: Acceleration
6:38
Gravity
7:31
Gravity
7:32
Formulas
8:44
Kinematics Formula 1
8:45
Kinematics Formula 2
9:32
Definitional Formulas
14:00
Example 1: Speed of a Rock Being Thrown
14:12
Example 2: How Long Does It Take for the Rock to Hit the Ground?
15:37
Example 3: Acceleration of a Biker
21:09
Example 4: Velocity and Displacement of a UFO
22:43
Multi-Dimensional Kinematics

29m 59s

Intro
0:00
0:07
Scalars and Vectors
0:08
A Note on Vectors
2:12
Indicating Vectors
2:13
Position
3:03
Position
3:04
Distance and Displacement
3:35
Distance and Displacement: Definitions
3:36
Distance and Displacement: Example
4:39
Speed and Velocity
8:57
Speed and Velocity: Definition & Formulas
8:58
Speed and Velocity: Example
10:06
Speed from Velocity
12:01
Speed from Velocity
12:02
Acceleration
14:09
Acceleration
14:10
Gravity
14:26
Gravity
14:27
Formulas
15:11
Formulas with Vectors
15:12
Example 1: Average Acceleration
16:57
Example 2A: Initial Velocity
19:14
Example 2B: How Long Does It Take for the Ball to Hit the Ground?
21:35
Example 2C: Displacement
26:46
Frames of Reference

18m 36s

Intro
0:00
Fundamental Example
0:25
Fundamental Example Part 1
0:26
Fundamental Example Part 2
1:20
General Case
2:36
Particle P and Two Observers A and B
2:37
Speed of P from A's Frame of Reference
3:05
3:22
Acceleration Shows the Change in Velocity
3:23
Acceleration when Velocity is Constant
3:48
Multi-Dimensional Case
4:35
Multi-Dimensional Case
4:36
Some Notes
5:04
Choosing the Frame of Reference
5:05
Example 1: What Velocity does the Ball have from the Frame of Reference of a Stationary Observer?
7:27
Example 2: Velocity, Speed, and Displacement
9:26
Example 3: Speed and Acceleration in the Reference Frame
12:44
Uniform Circular Motion

16m 34s

Intro
0:00
Centripetal Acceleration
1:21
Centripetal Acceleration of a Rock Being Twirled Around on a String
1:22
Looking Closer: Instantaneous Velocity and Tangential Velocity
2:35
Magnitude of Acceleration
3:55
Centripetal Acceleration Formula
5:14
You Say You Want a Revolution
6:11
What is a Revolution?
6:12
How Long Does it Take to Complete One Revolution Around the Circle?
6:51
Example 1: Centripetal Acceleration of a Rock
7:40
Example 2: Magnitude of a Car's Acceleration While Turning
9:20
Example 3: Speed of a Point on the Edge of a US Quarter
13:10
Section 2: Force
Newton's 1st Law

12m 37s

Intro
0:00
Newton's First Law/ Law of Inertia
2:45
A Body's Velocity Remains Constant Unless Acted Upon by a Force
2:46
Mass & Inertia
4:07
Mass & Inertia
4:08
Mass & Volume
5:49
Mass & Volume
5:50
Mass & Weight
7:08
Mass & Weight
7:09
Example 1: The Speed of a Rocket
8:47
Example 2: Which of the Following Has More Inertia?
10:06
Example 3: Change in Inertia
11:51
Newton's 2nd Law: Introduction

27m 5s

Intro
0:00
Net Force
1:42
Consider a Block That is Pushed On Equally From Both Sides
1:43
What if One of the Forces was Greater Than the Other?
2:29
The Net Force is All the Forces Put Together
2:43
Newton's Second Law
3:14
Net Force = (Mass) x (Acceleration)
3:15
Units
3:48
The Units of Newton's Second Law
3:49
Free-Body Diagram
5:34
Free-Body Diagram
5:35
Special Forces: Gravity (Weight)
8:05
Force of Gravity
8:06
Special Forces: Normal Force
9:22
Normal Force
9:23
Special Forces: Tension
10:34
Tension
10:35
Example 1: Force and Acceleration
12:19
Example 2: A 5kg Block is Pushed by Five Forces
13:24
Example 3: A 10kg Block Resting On a Table is Tethered Over a Pulley to a Free-Hanging 2kg Block
16:30
Newton's 2nd Law: Multiple Dimensions

27m 47s

Intro
0:00
Newton's 2nd Law in Multiple Dimensions
0:12
Newton's 2nd Law in Multiple Dimensions
0:13
Components
0:52
Components
0:53
Example: Force in Component Form
1:02
Special Forces
2:39
Review of Special Forces: Gravity, Normal Force, and Tension
2:40
Normal Forces
3:35
Why Do We Call It the Normal Forces?
3:36
Normal Forces on a Flat Horizontal and Vertical Surface
5:00
Normal Forces on an Incline
6:05
Example 1: A 5kg Block is Pushed By a Force of 3N to the North and a Force of 4N to the East
10:22
Example 2: A 20kg Block is On an Incline of 50° With a Rope Holding It In Place
16:08
Example 3: A 10kg Block is On an Incline of 20° Attached By Rope to a Free-hanging Block of 5kg
20:50

42m 5s

Intro
0:00
Block and Tackle Pulley System
0:30
A Single Pulley Lifting System
0:31
A Double Pulley Lifting System
1:32
2:59
Example 1: A Free-hanging, Massless String is Holding Up Three Objects of Unknown Mass
4:40
Example 2: An Object is Acted Upon by Three Forces
10:23
Example 3: A Chandelier is Suspended by a Cable From the Roof of an Elevator
17:13
Example 4: A 20kg Baboon Climbs a Massless Rope That is Attached to a 22kg Crate
23:46
Example 5: Two Blocks are Roped Together on Inclines of Different Angles
33:17
Newton's Third Law

16m 47s

Intro
0:00
Newton's Third Law
0:50
Newton's Third Law
0:51
Everyday Examples
1:24
Hammer Hitting a Nail
1:25
Swimming
2:08
Car Driving
2:35
Walking
3:15
Note
3:57
Newton's Third Law Sometimes Doesn't Come Into Play When Solving Problems: Reason 1
3:58
Newton's Third Law Sometimes Doesn't Come Into Play When Solving Problems: Reason 2
5:36
Example 1: What Force Does the Moon Pull on Earth?
7:04
Example 2: An Astronaut in Deep Space Throwing a Wrench
8:38
Example 3: A Woman Sitting in a Bosun's Chair that is Hanging from a Rope that Runs Over a Frictionless Pulley
12:51
Friction

50m 11s

Intro
0:00
Introduction
0:04
Our Intuition - Materials
0:30
Our Intuition - Weight
2:48
Our Intuition - Normal Force
3:45
The Normal Force and Friction
4:11
Two Scenarios: Same Object, Same Surface, Different Orientations
4:12
6:36
Friction as an Equation
7:23
Summing Up Friction
7:24
Friction as an Equation
7:36
The Direction of Friction
10:33
The Direction of Friction
10:34
A Quick Example
11:16
Which Block Will Accelerate Faster?
11:17
Static vs. Kinetic
14:52
Static vs. Kinetic
14:53
Static and Kinetic Coefficient of Friction
16:31
How to Use Static Friction
17:40
How to Use Static Friction
17:41
Some Examples of μs and μk
19:51
Some Examples of μs and μk
19:52
A Remark on Wheels
22:19
A Remark on Wheels
22:20
Example 1: Calculating μs and μk
28:02
Example 2: At What Angle Does the Block Begin to Slide?
31:35
Example 3: A Block is Against a Wall, Sliding Down
36:30
Example 4: Two Blocks Sitting Atop Each Other
40:16
Force & Uniform Circular Motion

26m 45s

Intro
0:00
Centripetal Force
0:46
Equations for Centripetal Force
0:47
Centripetal Force in Action
1:26
Where Does Centripetal Force Come From?
2:39
Where Does Centripetal Force Come From?
2:40
Centrifugal Force
4:05
Centrifugal Force Part 1
4:06
Centrifugal Force Part 2
6:16
Example 1: Part A - Centripetal Force On the Car
8:12
Example 1: Part B - Maximum Speed the Car Can Take the Turn At Without Slipping
8:56
Example 2: A Bucket Full of Water is Spun Around in a Vertical Circle
15:13
Example 3: A Rock is Spun Around in a Vertical Circle
21:36
Section 3: Energy
Work

28m 34s

Intro
0:00
Equivocation
0:05
Equivocation
0:06
Introduction to Work
0:32
Scenarios: 10kg Block on a Frictionless Table
0:33
Scenario: 2 Block of Different Masses
2:52
Work
4:12
Work and Force
4:13
Paralleled vs. Perpendicular
4:46
Work: A Formal Definition
7:33
An Alternate Formula
9:00
An Alternate Formula
9:01
Units
10:40
Unit for Work: Joule (J)
10:41
Example 1: Calculating Work of Force
11:32
Example 2: Work and the Force of Gravity
12:48
Example 3: A Moving Box & Force Pushing in the Opposite Direction
15:11
Example 4: Work and Forces with Directions
18:06
Example 5: Work and the Force of Gravity
23:16
Energy: Kinetic

39m 7s

Intro
0:00
Types of Energy
0:04
Types of Energy
0:05
Conservation of Energy
1:12
Conservation of Energy
1:13
What is Energy?
4:23
Energy
4:24
What is Work?
5:01
Work
5:02
Circular Definition, Much?
5:46
Circular Definition, Much?
5:47
Derivation of Kinetic Energy (Simplified)
7:44
Simplified Picture of Work
7:45
Consider the Following Three Formulas
8:42
Kinetic Energy Formula
11:01
Kinetic Energy Formula
11:02
Units
11:54
Units for Kinetic Energy
11:55
Conservation of Energy
13:24
Energy Cannot be Made or Destroyed, Only Transferred
13:25
Friction
15:02
How Does Friction Work?
15:03
Example 1: Velocity of a Block
15:59
Example 2: Energy Released During a Collision
18:28
Example 3: Speed of a Block
22:22
Example 4: Speed and Position of a Block
26:22
Energy: Gravitational Potential

28m 10s

Intro
0:00
Why Is It Called Potential Energy?
0:21
Why Is It Called Potential Energy?
0:22
Introduction to Gravitational Potential Energy
1:20
Consider an Object Dropped from Ever-Increasing heights
1:21
Gravitational Potential Energy
2:02
Gravitational Potential Energy: Derivation
2:03
Gravitational Potential Energy: Formulas
2:52
Gravitational Potential Energy: Notes
3:48
Conservation of Energy
5:50
Conservation of Energy and Formula
5:51
Example 1: Speed of a Falling Rock
6:31
Example 2: Energy Lost to Air Drag
10:58
Example 3: Distance of a Sliding Block
15:51
Example 4: Swinging Acrobat
21:32
Energy: Elastic Potential

44m 16s

Intro
0:00
Introduction to Elastic Potential
0:12
Elastic Object
0:13
Spring Example
1:11
Hooke's Law
3:27
Hooke's Law
3:28
Example of Hooke's Law
5:14
Elastic Potential Energy Formula
8:27
Elastic Potential Energy Formula
8:28
Conservation of Energy
10:17
Conservation of Energy
10:18
You Ain't Seen Nothin' Yet
12:12
You Ain't Seen Nothin' Yet
12:13
Example 1: Spring-Launcher
13:10
Example 2: Compressed Spring
18:34
Example 3: A Block Dangling From a Massless Spring
24:33
Example 4: Finding the Spring Constant
36:13
Power & Simple Machines

28m 54s

Intro
0:00
Introduction to Power & Simple Machines
0:06
What's the Difference Between a Go-Kart, a Family Van, and a Racecar?
0:07
Consider the Idea of Climbing a Flight of Stairs
1:13
Power
2:35
P= W / t
2:36
Alternate Formulas
2:59
Alternate Formulas
3:00
Units
4:24
Units for Power: Watt, Horsepower, and Kilowatt-hour
4:25
Block and Tackle, Redux
5:29
Block and Tackle Systems
5:30
Machines in General
9:44
Levers
9:45
Ramps
10:51
Example 1: Power of Force
12:22
Example 2: Power &Lifting a Watermelon
14:21
Example 3: Work and Instantaneous Power
16:05
Example 4: Power and Acceleration of a Race car
25:56
Section 4: Momentum
Center of Mass

36m 55s

Intro
0:00
Introduction to Center of Mass
0:04
Consider a Ball Tossed in the Air
0:05
Center of Mass
1:27
Definition of Center of Mass
1:28
Example of center of Mass
2:13
Center of Mass: Derivation
4:21
Center of Mass: Formula
6:44
Center of Mass: Formula, Multiple Dimensions
8:15
Center of Mass: Symmetry
9:07
Center of Mass: Non-Homogeneous
11:00
Center of Gravity
12:09
Center of Mass vs. Center of Gravity
12:10
Newton's Second Law and the Center of Mass
14:35
Newton's Second Law and the Center of Mass
14:36
Example 1: Finding The Center of Mass
16:29
Example 2: Finding The Center of Mass
18:55
Example 3: Finding The Center of Mass
21:46
Example 4: A Boy and His Mail
28:31
Linear Momentum

22m 50s

Intro
0:00
Introduction to Linear Momentum
0:04
Linear Momentum Overview
0:05
Consider the Scenarios
0:45
Linear Momentum
1:45
Definition of Linear Momentum
1:46
Impulse
3:10
Impulse
3:11
Relationship Between Impulse & Momentum
4:27
Relationship Between Impulse & Momentum
4:28
Why is It Linear Momentum?
6:55
Why is It Linear Momentum?
6:56
Example 1: Momentum of a Skateboard
8:25
Example 2: Impulse and Final Velocity
8:57
Example 3: Change in Linear Momentum and magnitude of the Impulse
13:53
Example 4: A Ball of Putty
17:07
Collisions & Linear Momentum

40m 55s

Intro
0:00
Investigating Collisions
0:45
Momentum
0:46
Center of Mass
1:26
Derivation
1:56
Extending Idea of Momentum to a System
1:57
Impulse
5:10
Conservation of Linear Momentum
6:14
Conservation of Linear Momentum
6:15
Conservation and External Forces
7:56
Conservation and External Forces
7:57
Momentum Vs. Energy
9:52
Momentum Vs. Energy
9:53
Types of Collisions
12:33
Elastic
12:34
Inelastic
12:54
Completely Inelastic
13:24
Everyday Collisions and Atomic Collisions
13:42
Example 1: Impact of Two Cars
14:07
Example 2: Billiard Balls
16:59
Example 3: Elastic Collision
23:52
Example 4: Bullet's Velocity
33:35
Section 5: Gravity
Gravity & Orbits

34m 53s

Intro
0:00
Law of Universal Gravitation
1:39
Law of Universal Gravitation
1:40
Force of Gravity Equation
2:14
Gravitational Field
5:38
Gravitational Field Overview
5:39
Gravitational Field Equation
6:32
Orbits
9:25
Orbits
9:26
The 'Falling' Moon
12:58
The 'Falling' Moon
12:59
Example 1: Force of Gravity
17:05
Example 2: Gravitational Field on the Surface of Earth
20:35
Example 3: Orbits
23:15
Example 4: Neutron Star
28:38
Section 6: Waves
Intro to Waves

35m 35s

Intro
0:00
Pulse
1:00
Introduction to Pulse
1:01
Wave
1:59
Wave Overview
2:00
Wave Types
3:16
Mechanical Waves
3:17
Electromagnetic Waves
4:01
Matter or Quantum Mechanical Waves
4:43
Transverse Waves
5:12
Longitudinal Waves
6:24
Wave Characteristics
7:24
Amplitude and Wavelength
7:25
Wave Speed (v)
10:13
Period (T)
11:02
Frequency (f)
12:33
v = λf
14:51
Wave Equation
16:15
Wave Equation
16:16
Angular Wave Number
17:34
Angular Frequency
19:36
Example 1: CPU Frequency
24:35
Example 2: Speed of Light, Wavelength, and Frequency
26:11
Example 3: Spacing of Grooves
28:35
Example 4: Wave Diagram
31:21
Waves, Cont.

52m 57s

Intro
0:00
Superposition
0:38
Superposition
0:39
Interference
1:31
Interference
1:32
Visual Example: Two Positive Pulses
2:33
Visual Example: Wave
4:02
Phase of Cycle
6:25
Phase Shift
7:31
Phase Shift
7:32
Standing Waves
9:59
Introduction to Standing Waves
10:00
Visual Examples: Standing Waves, Node, and Antinode
11:27
Standing Waves and Wavelengths
15:37
Standing Waves and Resonant Frequency
19:18
Doppler Effect
20:36
When Emitter and Receiver are Still
20:37
When Emitter is Moving Towards You
22:31
When Emitter is Moving Away
24:12
Doppler Effect: Formula
25:58
Example 1: Superposed Waves
30:00
Example 2: Superposed and Fully Destructive Interference
35:57
Example 3: Standing Waves on a String
40:45
Example 4: Police Siren
43:26
Example Sounds: 800 Hz, 906.7 Hz, 715.8 Hz, and Slide 906.7 to 715.8 Hz
48:49
Sound

36m 24s

Intro
0:00
Speed of Sound
1:26
Speed of Sound
1:27
Pitch
2:44
High Pitch & Low Pitch
2:45
Normal Hearing
3:45
Infrasonic and Ultrasonic
4:02
Intensity
4:54
Intensity: I = P/A
4:55
Intensity of Sound as an Outwardly Radiating Sphere
6:32
Decibels
9:09
Human Threshold for Hearing
9:10
Decibel (dB)
10:28
Sound Level β
11:53
Loudness Examples
13:44
Loudness Examples
13:45
Beats
15:41
Beats & Frequency
15:42
Audio Examples of Beats
17:04
Sonic Boom
20:21
Sonic Boom
20:22
Example 1: Firework
23:14
Example 2: Intensity and Decibels
24:48
Example 3: Decibels
28:24
Example 4: Frequency of a Violin
34:48
Light

19m 38s

Intro
0:00
The Speed of Light
0:31
Speed of Light in a Vacuum
0:32
Unique Properties of Light
1:20
Lightspeed!
3:24
Lightyear
3:25
Medium
4:34
Light & Medium
4:35
Electromagnetic Spectrum
5:49
Electromagnetic Spectrum Overview
5:50
Electromagnetic Wave Classifications
7:05
7:06
Microwave
8:30
Infrared and Visible Spectrum
9:02
Ultraviolet, X-rays, and Gamma Rays
9:33
So Much Left to Explore
11:07
So Much Left to Explore
11:08
Example 1: How Much Distance is in a Light-year?
13:16
Example 2: Electromagnetic Wave
16:50
Example 3: Radio Station & Wavelength
17:55
Section 7: Thermodynamics
Fluids

42m 52s

Intro
0:00
Fluid?
0:48
What Does It Mean to be a Fluid?
0:49
Density
1:46
What is Density?
1:47
Formula for Density: ρ = m/V
2:25
Pressure
3:40
Consider Two Equal Height Cylinders of Water with Different Areas
3:41
Definition and Formula for Pressure: p = F/A
5:20
Pressure at Depth
7:02
Pressure at Depth Overview
7:03
Free Body Diagram for Pressure in a Container of Fluid
8:31
Equations for Pressure at Depth
10:29
Absolute Pressure vs. Gauge Pressure
12:31
Absolute Pressure vs. Gauge Pressure
12:32
Why Does Gauge Pressure Matter?
13:51
Depth, Not Shape or Direction
15:22
Depth, Not Shape or Direction
15:23
Depth = Height
18:27
Depth = Height
18:28
Buoyancy
19:44
Buoyancy and the Buoyant Force
19:45
Archimedes' Principle
21:09
Archimedes' Principle
21:10
22:30
22:31
Example 1: Rock & Fluid
23:47
Example 2: Pressure of Water at the Top of the Reservoir
28:01
Example 3: Wood & Fluid
31:47
Example 4: Force of Air Inside a Cylinder
36:20
Intro to Temperature & Heat

34m 6s

Intro
0:00
Absolute Zero
1:50
Absolute Zero
1:51
Kelvin
2:25
Kelvin
2:26
Heat vs. Temperature
4:21
Heat vs. Temperature
4:22
Heating Water
5:32
Heating Water
5:33
Specific Heat
7:44
Specific Heat: Q = cm(∆T)
7:45
Heat Transfer
9:20
Conduction
9:24
Convection
10:26
11:35
Example 1: Converting Temperature
13:21
Example 2: Calories
14:54
Example 3: Thermal Energy
19:00
Example 4: Temperature When Mixture Comes to Equilibrium Part 1
20:45
Example 4: Temperature When Mixture Comes to Equilibrium Part 2
24:55
Change Due to Heat

44m 3s

Intro
0:00
Linear Expansion
1:06
Linear Expansion: ∆L = Lα(∆T)
1:07
Volume Expansion
2:34
Volume Expansion: ∆V = Vβ(∆T)
2:35
Gas Expansion
3:40
Gas Expansion
3:41
The Mole
5:43
Conceptual Example
5:44
7:30
Ideal Gas Law
9:22
Ideal Gas Law: pV = nRT
9:23
p = Pressure of the Gas
10:07
V = Volume of the Gas
10:34
n = Number of Moles of Gas
10:44
R = Gas Constant
10:58
T = Temperature
11:58
A Note On Water
12:21
A Note On Water
12:22
Change of Phase
15:55
Change of Phase
15:56
Change of Phase and Pressure
17:31
Phase Diagram
18:41
Heat of Transformation
20:38
Heat of Transformation: Q = Lm
20:39
Example 1: Linear Expansion
22:38
Example 2: Explore Why β = 3α
24:40
Example 3: Ideal Gas Law
31:38
Example 4: Heat of Transformation
38:03
Thermodynamics

27m 30s

Intro
0:00
First Law of Thermodynamics
1:11
First Law of Thermodynamics
1:12
Engines
2:25
Conceptual Example: Consider a Piston
2:26
Second Law of Thermodynamics
4:17
Second Law of Thermodynamics
4:18
Entropy
6:09
Definition of Entropy
6:10
Conceptual Example of Entropy: Stick of Dynamite
7:00
Order to Disorder
8:22
Order and Disorder in a System
8:23
The Poets Got It Right
10:20
The Poets Got It Right
10:21
Engines in General
11:21
Engines in General
11:22
Efficiency
12:06
Measuring the Efficiency of a System
12:07
Carnot Engine ( A Limit to Efficiency)
13:20
Carnot Engine & Maximum Possible Efficiency
13:21
Example 1: Internal Energy
15:15
Example 2: Efficiency
16:13
Example 3: Second Law of Thermodynamics
17:05
Example 4: Maximum Efficiency
20:10
Section 8: Electricity
Electric Force & Charge

41m 35s

Intro
0:00
Charge
1:04
Overview of Charge
1:05
Positive and Negative Charges
1:19
A Simple Model of the Atom
2:47
Protons, Electrons, and Neutrons
2:48
Conservation of Charge
4:47
Conservation of Charge
4:48
Elementary Charge
5:41
Elementary Charge and the Unit Coulomb
5:42
Coulomb's Law
8:29
Coulomb's Law & the Electrostatic Force
8:30
Coulomb's Law Breakdown
9:30
Conductors and Insulators
11:11
Conductors
11:12
Insulators
12:31
Conduction
15:08
Conduction
15:09
Conceptual Examples
15:58
Induction
17:02
Induction Overview
17:01
Conceptual Examples
18:18
Example 1: Electroscope
20:08
Example 2: Positive, Negative, and Net Charge of Iron
22:15
Example 3: Charge and Mass
27:52
Example 4: Two Metal Spheres
31:58
Electric Fields & Potential

34m 44s

Intro
0:00
Electric Fields
0:53
Electric Fields Overview
0:54
Size of q2 (Second Charge)
1:34
Size of q1 (First Charge)
1:53
Electric Field Strength: Newtons Per Coulomb
2:55
Electric Field Lines
4:19
Electric Field Lines
4:20
Conceptual Example 1
5:17
Conceptual Example 2
6:20
Conceptual Example 3
6:59
Conceptual Example 4
7:28
8:47
8:48
Why Does It Work?
9:33
Electric Potential Energy
11:40
Electric Potential Energy
11:41
Electric Potential
13:44
Electric Potential
13:45
Difference Between Two States
14:29
Electric Potential is Measured in Volts
15:12
Ground Voltage
16:09
Potential Differences and Reference Voltage
16:10
Ground Voltage
17:20
Electron-volt
19:17
Electron-volt
19:18
Equipotential Surfaces
20:29
Equipotential Surfaces
20:30
Equipotential Lines
21:21
Equipotential Lines
21:22
Example 1: Electric Field
22:40
Example 2: Change in Energy
24:25
Example 3: Constant Electrical Field
27:06
Example 4: Electrical Field and Change in Voltage
29:06
Example 5: Voltage and Energy
32:14
Electric Current

29m 12s

Intro
0:00
Electric Current
0:31
Electric Current
0:32
Amperes
1:27
Moving Charge
1:52
Conceptual Example: Electric Field and a Conductor
1:53
Voltage
3:26
Resistance
5:05
Given Some Voltage, How Much Current Will Flow?
5:06
Resistance: Definition and Formula
5:40
Resistivity
7:31
Resistivity
7:32
Resistance for a Uniform Object
9:31
Energy and Power
9:55
How Much Energy Does It take to Move These Charges Around?
9:56
What Do We Call Energy Per Unit Time?
11:08
Formulas to Express Electrical Power
11:53
Voltage Source
13:38
Introduction to Voltage Source
13:39
Obtaining a Voltage Source: Generator
15:15
Obtaining a Voltage Source: Battery
16:19
Speed of Electricity
17:17
Speed of Electricity
17:18
Example 1: Electric Current & Moving Charge
19:40
Example 2: Electric Current & Resistance
20:31
Example 3: Resistivity & Resistance
21:56
Example 4: Light Bulb
25:16
Electric Circuits

52m 2s

Intro
0:00
Electric Circuits
0:51
Current, Voltage, and Circuit
0:52
Resistor
5:05
Definition of Resistor
5:06
Conceptual Example: Lamps
6:18
Other Fundamental Components
7:04
Circuit Diagrams
7:23
Introduction to Circuit Diagrams
7:24
Wire
7:42
Resistor
8:20
Battery
8:45
Power Supply
9:41
Switch
10:02
Wires: Bypass and Connect
10:53
A Special Not in General
12:04
Example: Simple vs. Complex Circuit Diagram
12:45
Kirchoff's Circuit Laws
15:32
Kirchoff's Circuit Law 1: Current Law
15:33
Kirchoff's Circuit Law 1: Visual Example
16:57
Kirchoff's Circuit Law 2: Voltage Law
17:16
Kirchoff's Circuit Law 2: Visual Example
19:23
Resistors in Series
21:48
Resistors in Series
21:49
Resistors in Parallel
23:33
Resistors in Parallel
23:34
Voltmeter and Ammeter
28:35
Voltmeter
28:36
Ammeter
30:05
Direct Current vs. Alternating Current
31:24
Direct Current vs. Alternating Current
31:25
Visual Example: Voltage Graphs
33:29
Example 1: What Voltage is Read by the Voltmeter in This Diagram?
33:57
Example 2: What Current Flows Through the Ammeter When the Switch is Open?
37:42
Example 3: How Much Power is Dissipated by the Highlighted Resistor When the Switch is Open? When Closed?
41:22
Example 4: Design a Hallway Light Switch
45:14
Section 9: Magnetism
Magnetism

25m 47s

Intro
0:00
Magnet
1:27
Magnet Has Two Poles
1:28
Magnetic Field
1:47
Always a Dipole, Never a Monopole
2:22
Always a Dipole, Never a Monopole
2:23
Magnetic Fields and Moving Charge
4:01
Magnetic Fields and Moving Charge
4:02
Magnets on an Atomic Level
4:45
Magnets on an Atomic Level
4:46
Evenly Distributed Motions
5:45
Unevenly Distributed Motions
6:22
Current and Magnetic Fields
9:42
Current Flow and Magnetic Field
9:43
Electromagnet
11:35
Electric Motor
13:11
Electric Motor
13:12
Generator
15:38
A Changing Magnetic Field Induces a Current
15:39
Example 1: What Kind of Magnetic Pole must the Earth's Geographic North Pole Be?
19:34
Example 2: Magnetic Field and Generator/Electric Motor
20:56
Example 3: Destroying the Magnetic Properties of a Permanent Magnet
23:08
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Electric Force & Charge

• Charge, like mass, is a fundamental characteristic. It is tied to the atomic make-up of an object. The unit for charge is the coulomb (C).
• Charge comes in two types: positive and negative.
• Like charges repel each other (positive & positive; negative & negative), while opposite charges attract (positive & negative).
• Electrons have a negative charge, while protons have a positive charge (neutrons have no charge). The amount of charge is equal for electrons and protons, just differing signs. The amount is the elementary charge
 e = 1.602 ·10−19  C.
• Normally, objects come with an equal amount of positive and negative charge in them, giving the object a net charge of zero. However, it is possible to disrupt this and move some charge off one object on to another. This will leave us with one positively charged object and one negatively charged object.
• While it is possible to displace charge, it is not possible to destroy it. Charge is conserved, even if the two types are separated onto different objects.
• The amount of force caused by charge is given by Coulomb's law. This force is called the electrostatic force.
 F = k· q1 ·q2r2 ,
• q1 and q2 are the charges of the objects.
• r is the distance between the objects.
• k is the electrostatic constant:
 k = 8.99 ·109 N ·m2C2 .
• If the product is negative, they attract; if positive, they repel.
• The direction of the force is a direct line from one object to the other.
• A conductor is a material where it is very easy to move charge around the material. An insulator is one where it is very difficult to move charge around.
• If we have two conductors, one of them charged, and we touch them together, the charge on the first object will spread out evenly between the two of them. This is called conduction.
• If we have a charged object and we bring it near a conductor (without touching), we can induce a charge "imbalance" in the conductor. The opposite charge type will move to get near the charged object, while the same charge type will move to get away from the charged object.

Electric Force & Charge

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

• Intro 0:00
• Charge 1:04
• Overview of Charge
• Positive and Negative Charges
• A Simple Model of the Atom 2:47
• Protons, Electrons, and Neutrons
• Conservation of Charge 4:47
• Conservation of Charge
• Elementary Charge 5:41
• Elementary Charge and the Unit Coulomb
• Coulomb's Law 8:29
• Coulomb's Law & the Electrostatic Force
• Coulomb's Law Breakdown
• Conductors and Insulators 11:11
• Conductors
• Insulators
• Conduction 15:08
• Conduction
• Conceptual Examples
• Induction 17:02
• Induction Overview
• Conceptual Examples
• Example 1: Electroscope 20:08
• Example 2: Positive, Negative, and Net Charge of Iron 22:15
• Example 3: Charge and Mass 27:52
• Example 4: Two Metal Spheres 31:58

Transcription: Electric Force & Charge

Hi welcome back to educator.com. Today we’ll be talking about the electric force and charge.0000

Just to start off, you’re currently watching this video on some sort of computer that runs on electricity.0006

The screen is emitting light to your eyes because of electricity. The speakers are pumping out sound because of electricity.0011

The room that you’re currently in probably has lights that are run on electricity. You can probably look out your window and see street lights that are running on electricity.0018

On top of learning you almost certainly use electricity for warmth, transportation, food preparation, and storage, entertainment, communication, lighting things, and many, many other things.0027

Electricity makes up a fundamental part of our modern life. Without it we wouldn’t be able to have most of what we have and what we think of as common comforts, things that we just expect.0039

If we want to understand how all of the technology that makes up the modern world works, almost all of it we’re going to have to understand how electricity works.0051

The first step to understanding modern technology is understanding some of the basics’ behind electricity.0059

The foundation of electricity is the concept of charge. We denote charge with the letter q. Like mass charge is a fundamental characteristic of an object.0065

Also like mass, it’s deeply connected to the atomic make up of an object.0076

However, unlike mass charge comes in two opposite types. We call the two types positive charge and negative charge.0080

There’s not special reason why we call one negative and we call the other one positive. We could have chosen anything that just denoted their opposite nature.0088

We want something that’s opposite so that we remember the fact that they do come in two opposite versions.0095

It could have been anything really, it could have been anything. It doesn’t matter but it got set as positive and negative long ago by Benjamin Franklin who in addition to being one of the founding fathers, the United States of America, was also a pioneering scientist and did a huge amount of research.0101

The name suck and here we are using it today. Like charges repeal each other, so if you have two positive charges they push away from one another. Similarly if you have two negative charges, they also push away from one another.0118

However, opposite charges attract. So if you have a positive and a negative charge they attract each other.0133

This is also a little bit different than mass and gravity. When we were dealing with mass before any mass, two masses, they attract each other. There’s no repulsive version of gravity as far as we know.0139

As long as we’re going to have that we’re going to have this big difference between the way gravity works and the way electrical force works.0149

The electro static force, it’s going to work based on repulsion and attraction. It’s possible to do more than just pulling things in. It’s also possible to push things away with the electric force.0157

Before we talk more about electricity and the charge let’s talk about where the charge is coming from.0169

Let’s look at a simple model of the atom. At the center of an atom is a densely packed nucleus containing protons, which have positive charge and neutron which have no charge, neutral.0174

Pro for positive. Surrounding this nucleus is a moving cloud of electrons. Negative charge. Ele, electrical. There’s all these connections coming out.0185

What we’ve got here is we’ve got a model of the helium atom. Helium atom is atomic number 2. It’s got two protons in the middle and it’s got two electrons orbiting that nucleus in the center.0194

We’ve got the charges showing up, both in the center and the outside. A proton is much more massive than an electron but they each have the same amount of charge.0210

Even though they’re very different, one is moving, one is still, one’s massive, the other one is very not massive. They both have the same amount of charge in them.0220

But opposite types. Electrons have negative charge. Protons have positive charge.0230

Furthermore, generally atoms have the same number of electrons and protons. So they have a net charge of 0. Whenever we pull something off the periodic table we’re looking at it in general form of what it is when it has a full complement of its electrons.0236

They’re be slight changes as it can potentially gain or lose electrons. It can be disrupted; it can have this net charge of 0 but be disrupted through the gain or loss of electrons.0250

We call this ionizing. An atom can be ionized and if it’s ionized it can either loss or gain electrons, giving it a net charge.0262

If you gain electrons, you’ll be a negative ion. If you lose electrons, you’re a positive ion. Because if you lose electrons you’ll now have fewer electrons than you have protons so you’ll have less negative charge than you have positive charge and vice versa for the other direction.0272

Now we’ve got this idea of where charge is coming from. It’s possible to displace charge, we can move charge around and disrupted the starting neutrality of an object but it’s not possible to destroy charge.0288

Just like if we have an object we can pick it up and move part of it somewhere, we can scope of the dirt and we can move that dirt somewhere else but we can’t completely destroy that dirt.0300

That dirt will still be around. Just the same way with charge, we pick up some electrons, we move them somewhere else. We don’t get rid of the electrons, they get shifted.0311

Energy and momentum just like energy and momentum were we have conservation, charges always conserve.0319

When an ion is created it’s created because an electron leaves one particle and goes to another particle.0325

So we haven’t destroyed the electron, we haven’t destroyed the charge; we’ve just shifted it around. One particle will now become slightly negative and the other particle will become slightly positive by the amount of that electrons charge.0330

Just how much charge is in an electron or a proton? It’s the elementary charge. Since each one of these tiny, tiny things is where we get a charge from.0343

We know that a proton charges is equivalent to an electrons charge it’s going to be this tiny amount. They come like tiny, tiny grains of sand. Tiny grains of charge.0352

This elementary charge is 1.602 x 10^-19 coulombs where c is the letter for denoting coulomb, the unit for measuring charge.0363

Charge is measured with the coulomb. If it’s an electron we’d have a negative e, -1.602 x 10^-19 coulombs. If it were a proton it would be positive so we’ve have +1.602 x 10^-19 coulombs.0373

Notice this is a very small amount of charge. This is very small, 10^-19 is a very small, small number.0388

Since charge only comes in elementary charge chunks an object can have only an integer number of elementary charges. We can’t put on -4.7 of these charges, we can only put on 1 charge, 2 charge, 3 charge, 4 charge.0395

Or we could put on negative amounts, by putting on the negative version, an electron. We could have -1, -2, -3 e. Any of those possibilities but it is going to have to come in integer chunks of e.0410

However if we’re dealing with a large charge values such as one whole coulomb, remember an elementary charge is 10^-19, really tiny, tiny amount.0420

If we’re dealing with a large quantity of charge like say 1 whole coulomb of charge, that’s small elementary charge amount we can for the most part forget about the fact that it’s coming from this discreet nature.0431

We don’t have to worry about that chunky nature. The difference between 1 coulomb of charge and 1 coulomb plus one elementary charge is so slight we can effectively treat charge as continuous value without worrying about its chunky nature.0444

It’s like if you were to stick your hands under a water faucet. Each bit of the water is made up of a single water molecule, but because so much water is flowing, we don’t have to really treat it as if it’s a bunch of individual grains, a bunch of individual molecules bouncing off our hands.0457

We can treat it as its one collective continuous fluid quantity. So when we’re dealing with large quantities of charge, it’s okay to not worry about ‘Am I precise integer quantity?’0473

Because that is integer quantities are only going to be noticeable when we’re dealing with very small quantities of charge.0484

That said if we’re dealing with a very small quantity of charge you want to make sure that it is going to be an integer quantity of this e value.0489

If it’s not on this e value, this elementary charge value then it isn’t a possible amount because it’s got to come in these discreet chunks, otherwise it’s not possible to have it.0495

Charge is at its heart coming from either electrons or protons. It’s coming from the atomic level.0503

We know like charges repeal each other, opposite charges attract. We’ve talked about where charges are coming from.0511

But we haven’t talked about what the forces involved are. How much push do they have? How much pull do they have? What’s the strength of these forces?0517

The size of the force is given by coulombs law which is k x q1 x q2 over r squared. This force is called the electro static force.0524

The static is because it’s stationary, if we just have two objects sitting then its pushing for what they would be when we just look at statically, as opposed to flowing current charge which we will talk about later.0535

Current is the sort of thing that we’re used to in electricity that’s moving around in our walls, what we’re used to when we’re dealing with computers, when we’re dealing with electronic objects.0547

We’re used to dealing with current electricity as opposed to static electricity. Many of the same rules, pretty much all of the same rules will wind up applying. But that’s why it’s called the electro static force.0557

Because we’re just looking at what it is at one instant, how much is something pushing something else around.0566

Let’s investigate what all these letters mean. Q1 and Q2 are the charges of the objects. We have to know what the charges we’re dealing with are.0571

R is the distance between the objects, or more accurately the centers of the objects. If we’re dealing with two spheres we’re not going to look at the edges of the spheres closest, we’re going to look at the centers of those spheres.0580

For the most part we can just remember it as the distance between the objects. K is the electro static constant. This is just a special number that we have to memorize or write down or refer to.0590

K is equal to 8.99 x 10^9 Newtons times meters squared per coulomb. The reason why we’ve got…actually times over coulomb squared because what we want to make sure is that all of these things, the meters squared, they cancel out.0601

With the r squared, meters squared and r squared will cancel each other out. Similarly the coulomb squared will cancel out with q1 x q2 since they’re both in coulombs.0618

We’ll be left with something that’s just Newtons once we do all the calculations which is exactly what we want our force to come out in.0627

Finally notice this is the magnitude of the force. Remember force is still a vector. It’s up to us to point it in the correct direction. If we’ve got something…if we’ve got positive charges we need to remember that is going to be pushing away from one another.0633

If we’ve got two negative charges once again it’s going pushing away from each other. From one center to the other center, from one object to the other object, that’s the direction the force is going to move.0649

Finally, if we have a positive and a negative we can denote that with a negative force to show attract to one another. We can also just denote that in our force diagram that this is important and it can wind up screwing up some of our problems if we don’t catch that negative thing.0658

Conductors and insulators. It’s important to know how easily charge can flow through an object. Some materials hold onto their outermost electrons very loosely allowing them to pass charge around very easily.0672

Like a bucket brigade. We call such materials conductors. What I mean by a bucket brigade is we’ve each got each of these atoms. Say that for some reason there’s a force pushing electrons this way.0684

Then this electron can push into this one at which point it will get another electron pushed into this one. So another electron will get pushed into this one and so another electron will get pushed into this one.0697

So another electron will get pushed into this one. They each hand their electron up to the guy next to them. They’re able to very quickly move electrons around the surface of the material because they all simultaneously hand their electron up to the next guy next to them.0706

These electrons are freely moving so they conduct the electrons around easily. Metals in general make great conductors. Silver, copper, gold, aluminum are some of the best conductors.0720

Pretty much every metal and this is one of the things that makes a metal a metal is the fact that it is easily…easy for it to hand outermost electrons, its top level electrons around allowing it to conduct electrons around the surface of the metal very easily.0732

Or the surface of whatever conductor for [inaudible] conductors in general. On the flip slid we could be talking about an insulator. If a material holds onto its electrons very tightly, it’s very difficult for it to pass an electron around, for it to pass charge around.0748

We call such a material an insulator. Why do we call it an insulator? Because we call it insulator from when people were working on this originally, something that would insulate against the motion of charge.0762

That would keep charge from being able to move through it. This is a great thing if you’ve got copper wire with charge running through it and you want to make sure you can’t accidentally touch that copper wire and get shocked by the electrons going through you.0773

Instead you wrap an insulator around so you can now brush that copper wire and you won’t be able get shocked by it.0785

This is what those cords are where we’ve got cords that say, you want to plug in your microwave? There’s that plastic rubbery cord around it. That’s an insulator to keep you from touching the copper wires.0791

If we were to touch those copper wires we could potentially get hurt and the machine wouldn’t work if things wound up getting shorted it out.0800

So we’ve got to keep them insulated from one another to make sure that things can run smoothly and easily without accidentally connecting where they’re not supposed to connect.0806

Some great insulators include rubber, glass, air, and pure water; specifically it has to be chemically pure water. Just H2O. If salts get added, that suddenly allows the ability for electrons to be passed around.0815

One thing I’d like to point out is even though I keep saying electrons passed around; we can still look at this as the idea of positive charge being passed around.0828

Normally, the thing that’s really moving around is electrons, however if we had that bucket brigade idea. Well if everybody passes one electron to the right then at the end we’ve effectively just caused a positive to show up.0835

If everyone hands one guy to the right then the first guy to hand, who nobody hands something to him, we’ll he’s got one less electron which means he has more positive charge elementary unit.0850

He’s got one more positive charge unit…elementary charge. We can effectively move positive or negative charge around in a conductor.0860

We can treat it as if a positive thing is working just as much as a negative is moving around. In reality it’s only the electrons flowing around, but at the same time we can still treat it as if the positive is moving around.0868

From our point of view in measuring it we won’t be able to notice a difference between which specific type is moving. We’ll be able to tell if its negative or positive but we can treat it as that because there’s no way to fundamentally know which ones moving until we’ve got this atomic theory behind us.0879

That’s why Benjamin Franklin wound up naming the positive part for the protons; the thing that’s stationary is because at the time he didn’t know which one moved around and which one stayed still.0895

He just sort of accidentally bet it on the wrong horse, oh well. Conduction, if we have a conductive material, it makes it easy to pass charge around.0905

Since like charges repeal each other they want…of course they don’t actually have any real feelings in this, they’re just following basic laws of nature.0915

But we can treat it as if they’re trying to get away from each other. They want to get as far from each other as possible if they’re a like charge.0922

If a conductive object with charge on it touches around conductive material, the charge will spread out between the two things.0930

If there’s a lot of charge here, they’re trying to get away from each other but they’re stuck because they’re on a single object.0937

If they come along and they touch another object, suddenly they’ve got this other place to flee to. They’ve got more room to expand to.0942

They’ll expand onto it, they’ll conduct onto it and we’re going to have conduction onto the other material.0948

Some of the charge will leave the first object and go onto the second object. Here’s a great diagram to show this idea.0954

At beginning, we’ve got lots of negative charge on this first bar and we’ve got no charge on this second bar. The second bar has no charge on it but the first bar has a lot of negative charge on it.0962

We touch the two bars together and the electrons go “Oh man! More space to go to.” They all run over into there until they’re now all evenly distributed it.0974

The two bars are identical so they make it so that they distribute themselves evenly. If you’ve got two identical objects they’ll wind up distributing evenly because that’s the best way to be able to get as far away from each other as possible.0983

So they’ll distribute evenly over two identical objects, half of them run onto the second bar, the other half are like “Well I’m going to have at least as many neighbors were I go now, I might as well stay put.”0996

So they stay put, we separate the two bars and they’re still going to have the charges that they had in the second one because they’ve got no reason to run back onto the first one.1007

There’s no reason to get back on, they like having more room to spread out. They’re going to stay separated. This is a great example on conduction.1014

We can do a different thing though were we do induction. Similar to the idea, we’ve got this thing where the charges want something. They either want to away from each other if they’re the same or they want to be near each other if they’re the opposite.1023

That means if we’ve got charged object, if we bring that charged object near a conductor we’ll be able to induce a charge. What this means is that we assume; let’s say the conductor starts off neutral.1035

That means that it’s got positive and charges throughout. Well if we bring one type of charge over, well, all of the opposite charges are going to be like “Oh hey, let me get near you, let me get near you.”1048

They’ll all run up to it, they’ll try to get near it. All the guys who are the same as the thing that went there are going to be like “I don’t want to be near you.”1058

They’re going to run away from it and we’re going to get this separation. Some of the charge will get near the object that’s approaching and some of the charge will run away from the object that’s approaching.1065

Notice the net charge will remain the same in the object that’s the conductor, the conductor being induced. Then that charge will remain the same but the location of the charge will swirl around.1075

The conductor makes it very easy for charge to move around both positive and negative. It’s going to take that chance to be able to get as close to it or as far from the thing depending on what it once again quote on quote wants.1086

Here’s another visual example we can see, in the beginning we’ve got some negatively charged object over here and it’s far enough to not really any impact on this second object over here, the conductor.1098

We’ve got this conducting object and it’s just neutral and it’s got positive and negative charges mixed about and the negative charges don’t like each other but they like the positive charges, so things are basically pretty evenly distributed.1109

However, if we bring that negatively charged object really close to the conductor all of the sudden, all these positive guys, all these positive guys say “Hey, I want to be near to it.” They run up to the edge and they say “Let me get near it, let me get near it, let me near it.”1123

They can’t of course just jump onto it because we haven’t touched the two objects. We’re assuming that there’s some good insulator between them like air or the vacuum or something along those lines.1138

So they can’t get across to it but they can at least be near it, they’re pulled to it by the force of electricity. The positive charges are pulled to that side, at the same time the negative charges are repelled; they’re pushed away from the object.1149

They don’t want to be near it, they get pushed away in the other direction and so they’re going to be as far as they can. We’ve induced a charge, there’s’ no net charge change but in different locations of our conductor, we’re going to get different effective charges.1162

At least as long as the charged object is near the conductors. If the charged object where removed from the conductor, things would go back to being their mixed self because once again the positive don’t want to be near each other.1178

The negatives don’t want to be near other, so they’d spread out again and they’d once again mix with the other kind.1189

However, when we’ve got this super charged object moved near it things are going to break from their neutrality and they’re going to try and get near each other and they’re going to huddle up, pressing either towards it or trying to get away from it, depending.1194

Now we’re ready for some examples. An electroscope is a devise for measuring charge. It has a conducting rod that goes into a glass jar to keep out air motion, where it touches two very thin conducting plates.1210

By being in this glass jar air motion won’t be able to affect those glass plates so we know that the only thing that’s going to happen there is electrostatic force.1220

If the rod is touched by a charged object the plates will spring apart. Why?1228

Think about, if we’ve got a charged object, if we put a charged object up against this, lots of positive charge. Well some of the positive charge is going to get into it.1234

It’s a conductor so that positive charge is going to spread out as much as it can. It’s going to spread down to these plates.1245

These two plates both have positive charge. Positive charge repeal, they’re very thin, they’re very light weight and they’re going to swing up.1253

They’re going to push away from each other. What about…would it be possible to cause the plates to spring apart without actually touching the rod?1261

Would it be possible to cause the plates to swing apart without having to bring a conductor directly against it?1271

So here we’ve brought it directly against it. But we could do a similar thing where if we had a negative thing, we could induce a positive charge up here.1278

We can induce a positive charge. So all the positives will go ‘Oh hey, positive, positive, positive.’1290

We’ll get a bunch of positives up here; let’s erase this one just so we don’t have to get confused about which one we’re looking at.1295

All the positive charges, they run up there. When all the positive charges run up there, well where are the positive charges from the other place?1301

All the negative charges, they’re going to run down here. There’s going to be less positive charges down here.1311

Positive charges are going to be induced at the top without even needing to do contact. We don’t need direct conduction; we can induce the positive charge at the top.1318

Which means that we’re also going to have induced negative charge at the bottom. Once again we’ve got two kinds, opposite charges, they’re going to swing apart, they’re going to push apart from each other.1326

Second example. What’s the total positive charge in 50 grams of neutral uncharged iron, the total negative charge?1336

What’s the net charge in the iron? How much do all of the electrons in it make up for the negative charge? How much do all of the protons make up for the positive charge?1346

What would be the net charge? Well first off, we’re going to have to find out how many atoms of iron are in 50 grams.1355

We’re going to have to go to using mols. Since the atomic weight is 55.845 the number of mols, n is equal to the big mass, weight and grams divided by the atomic mass.1361

50 grams divided 55.845 and we get .895 mols. How many atoms are in a mol? The number of atoms in a mol, from before was 6.022 x 10^23 atoms per mol.1379

If you don’t remember this we talked about this in changes due to heat because we had to talk about it to get the ideal gas law across.1404

If you’re curious about understanding this more, go back; check out that section on mols. If you don’t need to know it that’s okay, you’ll still be able to get some of the idea of what’s going on here.1412

6.022 x 10^23 atoms per mol. If we want to know how many atoms we’ve got, we multiply these two together.1422

.895 x 6.022 x 10^23, that will tell us how many atoms of iron we have. So that gives us 5.39 x 10^23 atoms of iron.1430

The iron symbol is fe. So we know we’ve got 5.39 x 10^23 atoms of iron. In each one of these atoms there’s so number of protons and there is some number of electrons.1451

If the whole thing is neutrally charged then we know that we’re going to have to the same number of electrons in both….every atoms is going to have the same number of electrons as does protons.1462

What’s the number have to be? The atomic number is 26. We know it’s got 26 protons, 26 electrons for a neutrally charged one.1472

If we want to find out how many protons there are we take that 26 and we multiply it by that 5.39 x 10^23 number of atoms and that means since each atom has 26 protons we’re going to have a total number of protons of 1.4 x 10^25 protons.1482

We’re going to do the exact same operation to figure out the number of electrons. So 1.4 x 10^25 electrons.1505

Now we know how many electrons are running around in there, how many protons are running around in there.1514

How much charge does one proton have? How much charge does one electron have? Remember elementary charge is 1.602 x 10^-19 coulombs.1520

That’s a very small amount but we’ve got a whole bunch of protons. If we want to know what the positive charge is, it’s going to be that elementary charge times the number of protons we’ve got.1534

We’re going to have a positive charge from our protons of 2.24 x 10^6 coulombs. For our electrons we’re going to get the exact same thing.1547

Elementary charge times the number of electrons, same number of electrons except, is the elementary charge positive or negative now?1563

Remember we’re dealing with electrons so we’ve got negative charge. We’re going to get -2.24 x 10^6 coulombs.1568

Now we haven’t dealt much with electric forces yet but I’ll have you know, that is a huge amount of charge, like a terrifying amount of charge.1578

One coulomb is actually a lot of charge. One kilogram really, really common, we’re used to 1 kilogram in everyday things.1586

One coulomb charge just sitting static on an object, that’s a lot, lot of charge. It’s something you could potentially get but it’s a lot of charge.1592

10^6 coulombs is a gigantic amount and that’s just in 50 grams of iron. The important thing to note is that it’s 10^6 coulombs but there’s also it’s paired opposite. -2.24, so we’ve got positive and negative, so we’ve got it cancelled out.1603

The net charge is 0 coulombs. Since we’ve got neutral iron atoms, we know that we’ve got to have the same number of protons, same number of electrons.1620

So for every one of them they’re going to cancel each other out for the net charge. We’ve got massive positive charge and we’ve got massive negative charge, the total of each one is really, really large but when we look at it on the whole, we get this cancellation.1635

It’s just like when you’re sitting on a chair, you’ve got fairly large force pushing down on you, fairly large force pushing up on you, but in the end nothing really happens because you’re in static equilibrium.1647

Same thing going on in each one of these atoms at the same thing going on over the 50 grams as a whole. There’s this massive amount of charge there, massive potential forces going on, but because they’re intermixed they have no net effect and so the net charge cancels out as 0.1658

Two point masses in deep space. What the means is that they’re not going to be affected by any other forces than one another.1674

The first object has a mass of 4.7 x 10^6 kilograms and it has a charge -8.01 x 10^-12 coulombs. Not very much charge on it, but it’s a fairly massive object.1681

Second object has a pretty small mass, 100 kilograms. If the two objects are in static equilibrium what must be the charge q2 on the second object?1694

First thing to notice, what are the two…what forces are acting on this?1705

We’ve got two objects in deep space. Every object with a mass exerts gravitation pull on other massive objects.1711

We’ve got the force of gravity first. What’s the force of gravity? Force of gravity, magnitude for force of gravity is g x m1m2 / r², distance squared.1718

What else is there? Well we’ve got charge on one of them and we know that they’re in static equilibrium so we’ve got to have some other force canceling out that gravitation pull between them.1731

So we’ve got to have the electric force also here. Magnitude of the electric force is equal to k x q1q2 over that distance squared once again.1739

We’ve know that since f, the force of gravity and the force of electricity must be pushing in opposite directions and they have to be equal.1752

We know that the force of gravity, force of gravity is pulling in on both of them but there’s also has to be a force of electricity pushing out by the same amount.1761

Ultimately we’re going to have a cancellation of forces. If we’re going to get cancellation of forces that means that those two things must be equal.1773

If these two things are equal, what are we going to get out of it? We’ve got g m1 m2 / r² = k q1q2 / r².1783

Well first thing turns out we don’t need to know the distance. So if you’re worried that we didn’t know the distance, don’t worry about it. We can cancel out because it shows up on both sides.1799

At this point if we want to solve for q2 we just set q2 on one side. Q2 equals g m1 m2 / k q1.1806

At this point we need to remember what’s the gravitation constant? We go and we look it up in a manual or if we’re on a test hopefully we’ve memorized it or hopefully your teachers nice and lets you look up that thing, which I think is perfectly reasonable, but some teachers don’t.1819

6.67 x 10^-11. Then k, electrostatic constant is 8.99 x 10^9. We plug in all the numbers we have; 6.67 x 10^-11.1832

The mass of the first object is 4.7 x 10^6 times that 100 kilograms divided by 8.99 x 10^9 for k times that first charge, -8.01 x 10^-12.1851

If that gets a little bit hard to see but it will ultimately give us once we solve the whole thing out, but we’re going to get -0.435 coulombs.1875

What about the fact that we’ve got a negative number here? Should that worry us? No, not at all, we want a negative number.1887

If we hadn’t gotten a negative number we’d know something would have gone wrong. Because we know gravity has to be pulling together and for us to get a repulsive force from electricity we know that first object has a negative charge, the second has to have a negative charge.1893

Otherwise we won’t have that repulsive force. If we don’t have a repulsive force we’re not going to be able to cancel out the attractive force of gravity.1905

We’re able to find out that the charge has to be negative and then we can work it out and we get -0.435 coulombs.1912

Final example. We’ve got two identical metal spheres fixed in place, one here and another one here. At first they have an attractive force on each other of .15 Newtons.1919

We’re going to assume gravity’s not affecting this here, so the only thing attracting them is the force of electricity.1932

If they’ve got an attractive force, what’s that mean about those charges? They’ve got to be opposite. We know q1 and q2 have to be opposite.1938

One might be positive, one might be negative or it might be negative and then positive but we do know that they’re not the same type.1946

At first they’ve got an attractive force of .15 Newtons. They are then connected by a very thin wire which will allow for conduction.1953

One of them has a bunch of positive charge; the other one has a bunch of negative charge. Remember, positive charge wants to get away from all of its other positive charge friends.1962

The negative charge, I guess I should say more enemies because they’re trying to flee one another, and the negative charge is trying to get away from the other negatives.1970

They flee onto the other side and we’re going to get that they’re going to add together. We’re going to get it spread out. Since we’ve got identical metal spheres we know that we’re going to get identical spreading.1976

The final charge on each of them, q final, qf is going to be whatever was on q1 plus whatever was on q2 divided by 2.1986

It’s going to be the average of those two charges because it’s going to be evenly spread out. They’re both going to have to get the average otherwise we’re not going to have even spreading.1997

Notice that this means we’re going to have a pretty small amount of charge in the end because one of those was negative eventually.2005

The total amount of charge, total net charge is going to have to be less than what we had as the net charge on each of them originally.2010

The wire is removed and we’ll assume it’s a very thin wire so we don’t have to worry about any real charge being taken away on that wire once it goes away.2023

Because there would a few elementary charges strung along that but we’re going to assume it’s so thin, so small very few are going to wind up being left there, they’re almost entirely going to be on the spheres.2032

Finally the spheres repel each other with a force of .03 Newtons. If the charge on them is positive at the end, what were the initial charges?2045

At the end we’ve got positive charge so that means that we know qf is positive and now we’re ready to start working this out.2055

We’ve got the distance between them is .7 meters. The initial force is -.15 Newtons. That’s a really key thing to notice, is it isn’t positive because it’s attractive.2064

We haven’t really talked about how we tell where…we’ve only talked in terms of magnitude. A magnitude of -.15 is the same as +.15.2077

Notice if we plug in q1 as positive and q2 as negative or q1 as negative and q2 as positive, the important thing is that they have opposite signs.2085

If we plug in opposite sign charges we’re going to have to get a negative force from that formula otherwise things are going to break.2094

An attractive force is always going to be given by a negative value. That’s an important thing to keep in mind.2101

An attractive force will be spit out when we get a negative value and repulsive force will be spit out when we get a positive value.2107

A little bit different than what we were working with gravity where we always had attractive force because even though it always spit out positive.2115

It’s an important thing to keep in mind is suddenly it sort of comes up because the way we’ve talked about it. We’ve never introduced some of the mathematical machinery necessary to skip this issue but it is okay.2120

Just remember that it’s got to be negative if it’s attracting. Positive if it’s repulsive. Then it’s up to you to pay attention to where it’s pointing based on how the problem is set up.2133

If we’ve got this then we know that we can figure out qf now. Because force final is 0.03, a positive force because it’s repulsive.2147

K q final x q final, because its q final on both of them divided by that distance squared.2159

We solve for q final we’ll get r² 0.03 / k = qf². We take the square root of this; we plug in the numbers we’ve got.2167

0.7² x 0.03 divided by the electrostatic constant. Solve that out and notice that since we took the square root of both sides we could actually have +/-.2181

But we know for sure already this has to be a positive number because we were told that at the end charges were positive on each sphere.2199

We know that q final has to be wind up being positive. We’ve got 1.28 x 10^-6 coulombs.2209

That’s what the final charge is. Now we can use that to work to figuring out what the initial charges were.2220

Notice if qf equals q1 + q2 / 2 then we can solve for q2 to plug it in.2226

Lets look first at our initial force was -0.15 = k q1 q2 / r². To solve this equation we’re going to either have to get rid of q2 or get rid of q1.2234

To do that we use the fact that we know q final is equal to q1 + q2 / 2. So 2qf = q1 + q2.2251

We can say q2 = 2qf – q1. This isn’t a problem anymore because we know what qf is.2261

If we know what qf is we can throw that in down the road. Now we can just toss in what we’ve got.2277

-0.15 lets simplify this a little bit as we go. Move r², move that k. So we’re going to have q1 times what we sub in for q2, which is 2qf – q1.2282

We multiply that q1 over. We get r² -0.15. Let’s move that negative out front. Negative over k equals 2qf q1 – q1².2300

At this point we’ll move everything over to one side because what we’ve got now is we’ve got a quadratic formula….we’ve got a quadratic equation at this point.2320

We’re going to have to use either the quadratic formula or some sort of calculator that an impressive amount of algebraic solving in it.2331

We’ve got q1²; we keep moving this over because we want to have this equal to zero. Minus 2qf q1 – r² 0.15 / k.2338

Let’s substitute in all the values we know and it equals zero. We’ve got an equation here, so we substitute in all the values we know.2356

q1² - 2qf was 1.28 x 10^-6. Q1 - r² 0.7² 0.15 over the electrostatic constant 8.99 x 10^9 equals 0.2363

This is pretty ugly. I’ll be honest it’s not a very easy thing to solve. Not very fast, not very quick, but we’ve got some squared number, we’ve got some other number in front of….2387

We’ve got q1². Some number in front of q1 by itself and some constant. We can figure out what each one of these values is and we can either plug it into the quadratic formula or if you’ve got some sort of powerful calculator you could use an algebraic solver on that calculator to solve this whole equation.2403

If you do either one of those you’ll find out that the two possibilities for q1 is q1 is equal to either -1.85 x 10^-6 coulombs or +4.41 x 10^-6 coulombs.2419

We’ve got two different possibilities here. So how do we know which one to choose?2446

Well one thing to notice is that we could have also done this another way where we could have broken qf and we could have solved for q1 and we would have gotten q1 is equal to 2qf – q2.2451

So they’re symmetrical, so however we did this, one of them….this is going to be one of those charges will be -1.85 x 10^-6 and the other one is going to be other one.2464

We don’t know which charge was on which sphere and we can’t know that without getting a little more information but we do know that the two charges are going to have to be +4.41 x 10^-6 coulombs and -1.85 x 10^-6 coulombs.2474

Alright, hope that made sense, hope you have a better understanding of how electricity works and we’ve got a lot more to cover in it.2489

Alright, thanks, see you on educator.com later.2493

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