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Dan Fullerton

Dan Fullerton

Moving Charges In Magnetic Fields

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Table of Contents

I. Electricity
Electric Charge & Coulomb's Law

30m 48s

Intro
0:00
Objective
0:15
Electric Charges
0:50
Matter is Made Up of Atoms
0:52
Most Atoms are Neutral
1:02
Ions
1:11
Coulomb
1:18
Elementary Charge
1:34
Law of Conservation of Charge
2:03
Example 1
2:39
Example 2
3:42
Conductors and Insulators
4:41
Conductors Allow Electric Charges to Move Freely
4:43
Insulators Do Not Allow Electric Charges to Move Freely
4:50
Resistivity
4:58
Charging by Conduction
5:32
Conduction
5:37
Balloon Example
5:40
Charged Conductor
6:14
Example 3
6:28
The Electroscope
7:16
Charging by Induction
7:57
Bring Positive Rod Near Electroscope
8:08
Ground the Electroscope
8:27
Sever Ground Path and Remove Positive Rod
9:07
Example 4
9:39
Polarization and Electric Dipole Moment
11:46
Polarization
11:54
Electric Dipole Moment
12:05
Coulomb's Law
12:38
Electrostatic Force, Also Known as Coulombic Force
12:48
How Force of Attraction or Repulsion Determined
12:55
Formula
13:08
Coulomb's Law: Vector Form
14:18
Example 5
16:05
Example 6
18:25
Example 7
19:14
Example 8
23:21
Electric Fields

1h 19m 22s

Intro
0:00
Objectives
0:09
Electric Fields
1:33
Property of Space That Allows a Charged Object to Feel a Force
1:40
Detect the Presence of an Electric Field
1:51
Electric Field Strength Vector
2:03
Direction of the Electric Field Vector
2:21
Example 1
3:00
Visualizing the Electric Field
4:13
Electric Field Lines
4:56
E Field Due to a Point Charge
7:19
Derived from the Definition of the Electric Field and Coulomb's Law
7:24
Finding the Electric Field Due to Multiple Point Charges
8:37
Comparing Electricity to Gravity
8:51
Force
8:54
Field Strength
9:09
Constant
9:19
Charge Units vs. Mass Units
9:35
Attracts vs. Repel
9:44
Example 2
10:06
Example 3
17:25
Example 4
24:29
Example 5
25:23
Charge Densities
26:09
Linear Charge Density
26:26
Surface Charge Density
26:30
Volume Charge Density
26:47
Example 6
27:26
Example 7
37:07
Example 8
50:13
Example 9
54:01
Example 10
1:03:10
Example 11
1:13:58
Gauss's Law

52m 53s

Intro
0:00
Objectives
0:07
Electric Flux
1:16
Amount of Electric Field Penetrating a Surface
1:19
Symbol
1:23
Point Charge Inside a Hollow Sphere
4:31
Place a Point Charge Inside a Hollow Sphere of Radius R
4:39
Determine the Flux Through the Sphere
5:09
Gauss's Law
8:39
Total Flux
8:59
Gauss's Law
9:10
Example 1
9:53
Example 2
17:28
Example 3
22:37
Example 4
25:40
Example 5
30:49
Example 6
45:06
Electric Potential & Electric Potential Energy

1h 14m 3s

Intro
0:00
Objectives
0:08
Electric Potential Energy
0:58
Gravitational Potential Energy
1:02
Electric Potential Energy
1:11
Electric Potential
1:19
Example 1
1:59
Example 2
3:08
The Electron-Volt
4:02
Electronvolt
4:16
1 eV is the Amount of Work Done in Moving an Elementary Charge Through a Potential Difference of 1 Volt
4:26
Conversion Ratio
4:41
Example 3
4:52
Equipotential Lines
5:35
Topographic Maps
5:36
Lines Connecting Points of Equal Electrical Potential
5:47
Always Cross Electrical Field Lines at Right Angles
5:57
Gradient of Potential Increases As Equipotential Lines Get Closer
6:02
Electric Field Points from High to Low Potential
6:27
Drawing Equipotential Lines
6:49
E Potential Energy Due to a Point Charge
8:20
Electric Force from Electric Potential Energy
11:59
E Potential Due to a Point Charge
13:07
Example 4
14:42
Example 5
15:59
Finding Electric Field From Electric Potential
19:06
Example 6
23:41
Example 7
25:08
Example 8
26:33
Example 9
29:01
Example 10
31:26
Example 11
43:23
Example 12
51:51
Example 13
58:12
Electric Potential Due to Continuous Charge Distributions

1h 1m 28s

Intro
0:00
Objectives
0:10
Potential Due to a Charged Ring
0:27
Potential Due to a Uniformly Charged Desk
3:38
Potential Due to a Spherical Shell of Charge
11:21
Potential Due to a Uniform Solid Sphere
14:50
Example 1
23:08
Example 2
30:43
Example 3
41:58
Example 4
51:41
Conductors

20m 35s

Intro
0:00
Objectives
0:08
Charges in a Conductor
0:32
Charge is Free to Move Until the
0:36
All Charge Resides at Surface
2:18
Field Lines are Perpendicular to Surface
2:34
Electric Field at the Surface of a Conductor
3:04
Looking at Just the Outer Surface
3:08
Large Electric Field Where You Have the Largest Charge Density
3:59
Hollow Conductors
4:22
Draw Hollow Conductor and Gaussian Surface
4:36
Applying Gaussian Law
4:53
Any Hollow Conductor Has Zero Electric Field in Its Interior
5:24
Faraday Cage
5:35
Electric Field and Potential Due to a Conducting Sphere
6:03
Example 1
7:31
Example 2
12:39
Capacitors

41m 23s

Intro
0:00
Objectives
0:08
What is a Capacitor?
0:42
Electric Device Used to Store Electrical Energy
0:44
Place Opposite Charges on Each Plate
1:10
Develop a Potential Difference Across the Plates
1:14
Energy is Stored in the Electric Field Between the Plates
1:17
Capacitance
1:22
Ratio of the Charge Separated on the Plates of a Capacitor to the Potential Difference Between the Plates
1:25
Units of Capacitance
1:32
Farad
1:37
Formula
1:52
Calculating Capacitance
1:59
Assume Charge on Each Conductor
2:05
Find the Electric Field
2:11
Calculate V by Integrating the Electric Field
2:21
Utilize C=Q/V to Solve for Capitance
2:33
Example 1
2:44
Example 2
5:30
Example 3
10:46
Energy Stored in a Capacitor
15:25
Work is Done Charging a Capacitor
15:28
Solve For That
15:55
Field Energy Density
18:09
Amount of Energy Stored Between the Plates of a Capacitor
18:11
Example
18:25
Dielectrics
20:44
Insulating Materials Place Between Plates of Capacitor to Increase The Devices' Capacitance
20:47
Electric Field is Weakened
21:00
The Greater the Amount of Polarization The Greater the Reduction in Electric Field Strength
21:58
Dielectric Constant (K)
22:30
Formula
23:00
Net Electric Field
23:35
Key Take Away Point
23:50
Example 4
24:00
Example 5
25:50
Example 6
26:50
Example 7
28:53
Example 8
30:57
Example 9
32:55
Example 10
34:59
Example 11
37:35
Example 12
39:57
II. Current Electricity
Current & Resistance

17m 59s

Intro
0:00
Objectives
0:08
Electric Current
0:44
Flow Rate of Electric Charge
0:45
Amperes
0:49
Positive Current Flow
1:01
Current Formula
1:19
Drift Velocity
1:35
Constant Thermal Motion
1:39
Net Electron Flow
1:43
When Electric Field is Applied
1:49
Electron Drift Velocity
1:55
Derivation of Current Flow
2:12
Apply Electric Field E
2:20
Define N as the Volume Density of Charge Carriers
2:27
Current Density
4:33
Current Per Area
4:36
Formula
4:44
Resistance
5:14
Ratio of the Potential Drop Across an Object to the Current Flowing Through the Object
5:19
Ohmic Materials Follow Ohm's Law
5:23
Resistance of a Wire
6:05
Depends on Resistivity
6:09
Resistivity Relates to the Ability of a Material to Resist the Flow of Electrons
6:25
Refining Ohm's Law
7:22
Conversion of Electric Energy to Thermal Energy
8:23
Example 1
9:54
Example 2
10:54
Example 3
11:26
Example 4
14:41
Example 5
15:24
Circuits I: Series Circuits

29m 8s

Intro
0:00
Objectives
0:08
Ohm's Law Revisited
0:39
Relates Resistance, Potential Difference, and Current Flow
0:39
Formula
0:44
Example 1
1:09
Example 2
1:44
Example 3
2:15
Example 4
2:56
Electrical Power
3:26
Transfer of Energy Into Different Types
3:28
Light Bulb
3:37
Television
3:41
Example 5
3:49
Example 6
4:27
Example 7
5:12
Electrical Circuits
5:42
Closed-Loop Path Which Current Can Flow
5:43
Typically Comprised of Electrical Devices
5:52
Conventional Current Flows from High Potential to Low Potential
6:04
Circuit Schematics
6:26
Three-dimensional Electrical Circuits
6:37
Source of Potential Difference Required for Current to Flow
7:29
Complete Conducting Paths
7:42
Current Only Flows in Complete Paths
7:43
Left Image
7:46
Right Image
7:56
Voltmeters
8:25
Measure the Potential Difference Between Two Points in a Circuit
8:29
Can Remove Voltmeter from Circuit Without Breaking the Circuit
8:47
Very High Resistance
8:53
Ammeters
9:31
Measure the Current Flowing Through an Element of a Circuit
9:32
Very Low Resistance
9:46
Put Ammeter in Correctly
10:00
Example 8
10:24
Example 9
11:39
Example 10
12:59
Example 11
13:16
Series Circuits
13:46
Single Current Path
13:49
Removal of Any Circuit Element Causes an Open Circuit
13:54
Kirchhoff's Laws
15:48
Utilized in Analyzing Circuits
15:54
Kirchhoff's Current Law
15:58
Junction Rule
16:02
Kirchhoff's Voltage Law
16:30
Loop Rule
16:49
Example 12
16:58
Example 13
17:32
Basic Series Circuit Analysis
18:36
Example 14
22:06
Example 15
22:29
Example 16
24:02
Example 17
26:47
Circuits II: Parallel Circuits

39m 9s

Intro
0:00
Objectives
0:16
Parallel Circuits
0:38
Multiple Current Paths
0:40
Removal of a Circuit Element May Allow Other Branches of the Circuit to Continue Operating
0:44
Draw a Simple Parallel Circuit
1:02
Basic Parallel Circuit Analysis
3:06
Example 1
5:58
Example 2
8:14
Example 3
9:05
Example 4
11:56
Combination Series-Parallel Circuits
14:08
Circuit Doesn't Have to be Completely Serial or Parallel
14:10
Look for Portions of the Circuit With Parallel Elements
14:15
Lead to Systems of Equations to Solve
14:42
Analysis of a Combination Circuit
14:51
Example 5
20:23
Batteries
28:49
Electromotive Force
28:50
Pump for Charge
29:04
Ideal Batteries Have No Resistance
29:10
Real Batteries and Internal Resistance
29:20
Terminal Voltage in Real Batteries
29:33
Ideal Battery
29:50
Real Battery
30:25
Example 6
31:10
Example 7
33:23
Example 8
35:49
Example 9
38:43
RC Circuits: Steady State

34m 3s

Intro
0:00
Objectives
0:17
Capacitors in Parallel
0:51
Store Charge on Plates
0:52
Can Be Replaced with an Equivalent Capacitor
0:56
Capacitors in Series
1:12
Must Be the Same
1:13
Can Be Replaced with an Equivalent Capacitor
1:15
RC Circuits
1:30
Comprised of a Source of Potential Difference, a Resistor Network, and Capacitor
1:31
RC Circuits from the Steady-State Perspective
1:37
Key to Understanding RC Circuit Performance
1:48
Charging an RC Circuit
2:08
Discharging an RC Circuit
6:18
The Time Constant
8:49
Time Constant
8:58
By 5 Time Constant
9:19
Example 1
9:45
Example 2
13:27
Example 3
16:35
Example 4
18:03
Example 5
19:39
Example 6
26:14
RC Circuits: Transient Analysis

1h 1m 7s

Intro
0:00
Objectives
0:13
Charging an RC Circuit
1:11
Basic RC Circuit
1:15
Graph of Current Circuit
1:29
Graph of Charge
2:17
Graph of Voltage
2:34
Mathematically Describe the Charts
2:56
Discharging an RC Circuit
13:29
Graph of Current
13:47
Graph of Charge
14:08
Graph of Voltage
14:15
Mathematically Describe the Charts
14:30
The Time Constant
20:03
Time Constant
20:04
By 5 Time Constant
20:14
Example 1
20:39
Example 2
28:53
Example 3
27:02
Example 4
44:29
Example 5
55:24
III. Magnetism
Magnets

8m 38s

Intro
0:00
Objectives
0:08
Magnetism
0:35
Force Caused by Moving Charges
0:36
Dipoles
0:40
Like Poles Repel, Opposite Poles Attract
0:53
Magnetic Domains
0:58
Random Domains
1:04
Net Magnetic Field
1:26
Example 1
1:40
Magnetic Fields
2:03
Magnetic Field Strength
2:04
Magnets are Polarized
2:16
Magnetic Field Lines
2:53
Show the Direction the North Pole of a Magnet Would Tend to Point if Placed on The Field
2:54
Direction
3:25
Magnetic Flux
3:41
The Compass
4:05
Earth is a Giant Magnet
4:07
Earth's Magnetic North Pole
4:10
Compass Lines Up with the Net Magnetic Field
4:48
Magnetic Permeability
5:00
Ratio of the magnetic Field Strength Induced in a Material to the Magnetic Field Strength of the Inducing Field
5:01
Free Space
5:13
Permeability of Matter
5:41
Highly Magnetic Materials
5:47
Magnetic Dipole Moment
5:54
The Force That a Magnet Can Exert on Moving Charges
5:59
Relative Strength of a Magnet
6:04
Example 2
6:26
Example 3
6:52
Example 4
7:32
Example 5
7:57
Moving Charges In Magnetic Fields

29m 7s

Intro
0:00
Objectives
0:08
Magnetic Fields
0:57
Vector Quantity
0:59
Tesla
1:08
Gauss
1:14
Forces on Moving Charges
1:30
Magnetic Force is Always Perpendicular to the Charged Objects Velocity
1:31
Magnetic Force Formula
2:04
Magnitude of That
2:20
Image
2:29
Direction of the Magnetic Force
3:54
Right-Hand Rule
3:57
Electron of Negative Charge
4:04
Example 1
4:51
Example 2
6:58
Path of Charged Particles in B Fields
8:07
Magnetic Force Cannot Perform Work on a Moving Charge
8:08
Magnetic Force Can Change Its Direction
8:11
Total Force on a Moving Charged Particle
9:40
E Field
9:50
B Field
9:54
Lorentz Force
9:57
Velocity Selector
10:33
Charged Particle in Crosses E and B Fields Can Undergo Constant Velocity Motion
10:37
Particle Can Travel Through the Selector Without Any Deflection
10:49
Mass Spectrometer
12:21
Magnetic Fields Accelerate Moving Charges So That They Travel in a Circle
12:26
Used to Determine the Mass of An Unknown Particle
12:32
Example 3
13:11
Example 4
15:01
Example 5
16:44
Example 6
17:33
Example 7
19:12
Example 8
19:50
Example 9
24:02
Example 10
25:21
Forces on Current-Carrying Wires

17m 52s

Intro
0:00
Objectives
0:08
Forces on Current-Carrying Wires
0:42
Moving Charges in Magnetic Fields Experience Forces
0:45
Current in a Wire is Just Flow of Charges
0:49
Direction of Force Given by RHR
4:04
Example 1
4:22
Electric Motors
5:59
Example 2
8:14
Example 3
8:53
Example 4
10:09
Example 5
11:04
Example 6
12:03
Magnetic Fields Due to Current-Carrying Wires

24m 43s

Intro
0:00
Objectives
0:08
Force on a Current-Carrying Wire
0:38
Magnetic Fields Cause a Force on Moving Charges
0:40
Current Carrying Wires
0:44
How to Find the Force
0:55
Direction Given by the Right Hand Rule
1:04
Example 1
1:17
Example 2
2:26
Magnetic Field Due to a Current-Carrying Wire
4:20
Moving Charges Create Magnetic Fields
4:24
Current-Carrying Wires Carry Moving Charges
4:27
Right Hand Rule
4:32
Multiple Wires
4:51
Current-Carrying Wires Can Exert Forces Upon Each Other
4:58
First Right Hand Rule
5:15
Example 3
6:46
Force Between Parallel Current Carrying Wires
8:01
Right Hand Rules to Determine Force Between Parallel Current Carrying Wires
8:03
Find Magnetic Field Due to First Wire, Then Find Direction of Force on 2nd Wire
8:08
Example
8:20
Gauss's Law for Magnetism
9:26
Example 4
10:35
Example 5
12:57
Example 6
14:19
Example 7
16:50
Example 8
18:15
Example 9
18:43
The Biot-Savart Law

21m 50s

Intro
0:00
Objectives
0:07
Biot-Savart Law
0:24
Brute Force Method
0:49
Draw It Out
0:54
Diagram
1:35
Example 1
3:43
Example 2
7:02
Example 3
14:31
Ampere's Law

26m 31s

Intro
0:00
Objectives
0:07
Ampere's Law
0:27
Finds the Magnetic Field Due to Current Flowing in a Wire in Situations of Planar and Cylindrical Symmetry
0:30
Formula
0:40
Example
1:00
Example 1
2:19
Example 2
4:08
Example 3
6:23
Example 4
8:06
Example 5
11:43
Example 6
13:40
Example 7
17:54
Magnetic Flux

7m 24s

Intro
0:00
Objectives
0:07
Magnetic Flux
0:31
Amount of Magnetic Field Penetrating a Surface
0:32
Webers
0:42
Flux
1:07
Total Magnetic Flux
1:27
Magnetic Flux Through Closed Surfaces
1:51
Gauss's Law for Magnetism
2:20
Total Flux Magnetic Flux Through Any Closed Surface is Zero
2:23
Formula
2:45
Example 1
3:02
Example 2
4:26
Faraday's Law & Lenz's Law

1h 4m 33s

Intro
0:00
Objectives
0:08
Faraday's Law
0:44
Faraday's Law
0:46
Direction of the Induced Current is Given by Lenz's Law
1:09
Formula
1:15
Lenz's Law
1:49
Lenz's Law
2:14
Lenz's Law
2:16
Example
2:30
Applying Lenz's Law
4:09
If B is Increasing
4:13
If B is Decreasing
4:30
Maxwell's Equations
4:55
Gauss's Law
4:59
Gauss's Law for Magnetism
5:16
Ampere's Law
5:26
Faraday's Law
5:39
Example 1
6:14
Example 2
9:36
Example 3
11:12
Example 4
19:33
Example 5
26:06
Example 6
31:55
Example 7
42:32
Example 8
48:08
Example 9
55:50
IV. Inductance, RL Circuits, and LC Circuits
Inductance

6m 41s

Intro
0:00
Objectives
0:08
Self Inductance
0:25
Ability of a Circuit to Oppose the Magnetic Flux That is Produced by the Circuit Itself
0:27
Changing Magnetic Field Creates an Induced EMF That Fights the Change
0:37
Henrys
0:44
Function of the Circuit's Geometry
0:53
Calculating Self Inductance
1:10
Example 1
3:40
Example 2
5:23
RL Circuits

42m 17s

Intro
0:00
Objectives
0:11
Inductors in Circuits
0:49
Inductor Opposes Current Flow and Acts Like an Open Circuit When Circuit is First Turned On
0:52
Inductor Keeps Current Going and Acts as a Short
1:04
If the Battery is Removed After a Long Time
1:16
Resister Dissipates Power, Current Will Decay
1:36
Current in RL Circuits
2:00
Define the Diagram
2:03
Mathematically Solve
3:07
Voltage in RL Circuits
7:51
Voltage Formula
7:52
Solve
8:17
Rate of Change of Current in RL Circuits
9:42
Current and Voltage Graphs
10:54
Current Graph
10:57
Voltage Graph
11:34
Example 1
12:25
Example 2
23:44
Example 3
34:44
LC Circuits

9m 47s

Intro
0:00
Objectives
0:08
LC Circuits
0:30
Assume Capacitor is Fully Charged When Circuit is First Turned On
0:38
Interplay of Capacitor and Inductor Creates an Oscillating System
0:42
Charge in LC Circuit
0:57
Current and Potential in LC Circuits
7:14
Graphs of LC Circuits
8:27
V. Maxwell's Equations
Maxwell's Equations

3m 38s

Intro
0:00
Objectives
0:07
Maxwell's Equations
0:19
Gauss's Law
0:20
Gauss's Law for Magnetism
0:44
Faraday's Law
1:00
Ampere's Law
1:18
Revising Ampere's Law
1:49
Allows Us to Calculate the Magnetic Field Due to an Electric Current
1:50
Changing Electric Field Produces a Magnetic Field
1:58
Conduction Current
2:33
Displacement Current
2:44
Maxwell's Equations (Complete)
2:58
VI. Sample AP Exams
1998 AP Practice Exam: Multiple Choice Questions

32m 33s

Intro
0:00
1998 AP Practice Exam Link
0:11
Multiple Choice 36
0:36
Multiple Choice 37
2:07
Multiple Choice 38
2:53
Multiple Choice 39
3:32
Multiple Choice 40
4:37
Multiple Choice 41
4:43
Multiple Choice 42
5:22
Multiple Choice 43
6:00
Multiple Choice 44
8:09
Multiple Choice 45
8:27
Multiple Choice 46
9:03
Multiple Choice 47
9:30
Multiple Choice 48
10:19
Multiple Choice 49
10:47
Multiple Choice 50
12:25
Multiple Choice 51
13:10
Multiple Choice 52
15:06
Multiple Choice 53
16:01
Multiple Choice 54
16:44
Multiple Choice 55
17:10
Multiple Choice 56
19:08
Multiple Choice 57
20:39
Multiple Choice 58
22:24
Multiple Choice 59
22:52
Multiple Choice 60
23:34
Multiple Choice 61
24:09
Multiple Choice 62
24:40
Multiple Choice 63
25:06
Multiple Choice 64
26:07
Multiple Choice 65
27:26
Multiple Choice 66
28:32
Multiple Choice 67
29:14
Multiple Choice 68
29:41
Multiple Choice 69
31:23
Multiple Choice 70
31:49
1998 AP Practice Exam: Free Response Questions

29m 55s

Intro
0:00
1998 AP Practice Exam Link
0:14
Free Response 1
0:22
Free Response 2
10:04
Free Response 3
16:22
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Lecture Comments (2)

1 answer

Last reply by: Professor Dan Fullerton
Mon Nov 24, 2014 6:08 AM

Post by QuangNguyen VoHuynh on November 24, 2014

I would like to ask the reason why magnetic force cannot perform work? Is it because the force creates a circular motion, so that the displacement is zero?

Moving Charges In Magnetic Fields

  • Magnetic field strength (B) is a vector quantity. Its units are Tesla (T).
  • Magnet fields exert forces on moving charges proportional to the charge, the velocity, and the magnetic field strength. The magnetic force on a moving charge is always perpendicular to both the charge's velocity and the magnetic field.
  • F=q(vxB)=qvBsinθ
  • The direction of the magnetic force on a moving charge is given by the right hand rule. Point the fingers of your right hand in the direction of a positive particle’s velocity. Curl your fingers inward in the direction of the magnetic field, and your thumb will point in the direction of the force on the charged particle. For a negatively charged particle, use your left hand.
  • A magnetic field can do no work on a moving charged particle, but it can change the particle’s direction.
  • A mass spectrometer bends a moving charge using the magnetic force to determine the mass of unknown charged particles.
  • A velocity selector utilizes a combination of magnetic and electric fields to allow a charged particle with a specific velocity to pass through in a straight line, while particles of other speeds and charges are deflected.

Moving Charges In Magnetic Fields

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
  • Objectives 0:08
  • Magnetic Fields 0:57
    • Vector Quantity
    • Tesla
    • Gauss
  • Forces on Moving Charges 1:30
    • Magnetic Force is Always Perpendicular to the Charged Objects Velocity
    • Magnetic Force Formula
    • Magnitude of That
    • Image
  • Direction of the Magnetic Force 3:54
    • Right-Hand Rule
    • Electron of Negative Charge
  • Example 1 4:51
  • Example 2 6:58
  • Path of Charged Particles in B Fields 8:07
    • Magnetic Force Cannot Perform Work on a Moving Charge
    • Magnetic Force Can Change Its Direction
  • Total Force on a Moving Charged Particle 9:40
    • E Field
    • B Field
    • Lorentz Force
  • Velocity Selector 10:33
    • Charged Particle in Crosses E and B Fields Can Undergo Constant Velocity Motion
    • Particle Can Travel Through the Selector Without Any Deflection
  • Mass Spectrometer 12:21
    • Magnetic Fields Accelerate Moving Charges So That They Travel in a Circle
    • Used to Determine the Mass of An Unknown Particle
  • Example 3 13:11
  • Example 4 15:01
  • Example 5 16:44
  • Example 6 17:33
  • Example 7 19:12
  • Example 8 19:50
  • Example 9 24:02
  • Example 10 25:21

Transcription: Moving Charges In Magnetic Fields

Hello, everyone, and welcome back to www.educator.com.0000

In this lesson, we are going to talk about moving charges in magnetic fields.0004

Our objectives include calculating the magnitude and direction of the magnetic force on moving charges in terms of their charge,0008

their velocity, and the magnetic field strength.0014

Explaining why the magnetic force cannot perform any work on these charges.0019

We will talk about how we deduce the direction of the magnetic field from information about the forces0024

experienced by charged particles moving through the fields, getting into our right hand rules.0029

We will derive and apply the formula for the radius of the circular path of the charge moving perpendicular to a uniform magnetic field.0033

Finally, describing under what conditions particles would move with constant velocity through across the electric and magnetic fields.0042

Talking about there is what we are going to call the velocity selector.0049

Let us get in there and first of all get a few more details about magnetic fields.0053

Magnetic field strength capital B, is a vector quantity.0058

We said the units are tesla or a tesla is N-s/ C-m.0062

A tesla is a very strong magnetic field as we mentioned before.0068

There is also a common nonstandard unit which is called the Gauss.0073

Where 1 Gauss is 10⁻⁴ tesla, that should be an exponent 10⁻⁴ T.0078

The earth's magnetic field strength is right about ½ Gauss.0085

The magnetic force is always perpendicular to the charged objects velocity.0092

Because that force is always perpendicular to the velocity,0096

the magnetic force on a moving charge cannot be applied in the direction of the object’s displacement.0100

You cannot do any work on a moving charge.0106

Remember, work is force × displacement.0109

It is force dotted with displacement, because the force and the displacement are always going to be perpendicular,0111

you cannot do any work with that magnetic field.0117

You can, however, change its direction.0120

The magnetic force which is F vector and often time you see the subscript M for magnetic,0124

or you may see FB for magnetic.0130

It is the charge × its velocity × with the magnetic field vector.0134

Or the magnitude of that is going to be QVB × sin θ, where θ is the angle between your velocity and your magnetic field.0140

If you look over here on the right, we have a positively charge particle Q, moving with some velocity V as shown here.0150

It is doing so in the uniform magnetic field.0157

And the magnetic field symbol, we have here the dot with a circle around it and it is coming out of the page,0159

out of the screen in front of you.0165

If instead we saw something like an X with a circle around it, that would indicate it is going into the page or into the screen.0167

You are seeing, if you look over here, you are looking at the point of an arrow coming toward you.0174

You see the point first.0180

If it is going away from you, you see the X, the fletching on the arrow.0182

That is what that symbol means, it is showing you a vector in 3 dimensions into or out of the plane.0185

In this case, we have a magnetic field coming out of the plane.0191

The way we figure out the direction of the force, QV × B.0194

If you remember from our math review with × products, point the fingers of your right hand in the direction of the velocity0198

and bend your fingers inward in the direction of the magnetic field,0205

your thumb is going to point in the direction of the magnetic force on that charged particle.0209

In this case, if I use that right hand rule, point the fingers of my right hand in the direction of the velocity.0215

Bend them in the direction of the magnetic field, I end up with a force down and into the right on the page.0221

Perpendicular to the end, perpendicular to the magnetic field.0228

Just covering that again, as we look at this right hand rule, the direction of the force is given by a right hand rule.0236

If I say a positively charged particle, you can use your right hand.0242

If you are looking at something like an electron, something with a negative charge,0245

you can either use a right hand and go in the opposite direction of what your thumb points, or even easier user your left hand if it is negatively charged particle.0248

You are going to point the fingers of your right hand in the direction of a positive particle’s velocity.0258

Curl your fingers inward in the direction of the magnetic field.0265

Once you have done that, your thumb is going to point in the direction of the force on that charged particle, as shown in the diagram here.0269

Fingers in the direction of the velocity bend inward in the direction of the magnetic field0278

and your thumb points in the direction of that magnetic force on the moving charged particle.0282

Let us take an example.0292

Let us look at the force on an electron.0294

An electron moves at 2,000,000 m/ s perpendicular to a magnetic field with the flux density of 2 tesla.0296

What is the magnitude of the magnetic force on the electron?0305

Starting with what we know, its velocity is 2,000,000 m/ s.0308

Our magnetic field strength is 2 tesla, and our charge if it is an electronic is -1.6 × 10 ⁻19 C.0316

And because we are worried about the magnitude of the charge, I'm not going to worry about the negatives.0330

Our magnetic force which I like to write as FB but you could use FM, is Q the charge × V × B,0334

or if we are looking for the magnitude, which implies then that the magnitude of the magnetic force0346

on our charged particle is going to be Q VB sin θ, where θ is the angle between V and B.0353

It says in the problem that those are perpendicular.0361

If θ is 90°, that means its sin θ is sin 90° which is going to be 1.0363

That term goes away.0372

The magnitude of our magnetic force is our charge 1.6 × 10 ⁻19 C × our velocity 2,000,000 m/ s × our magnetic field strength 2 tesla.0376

And I come up with a magnitude of the magnetic force on our moving charge particle of about 6.4 × 10 ⁻13 N.0394

We did the magnitude problem here.0413

Let us take a look and see if we can figure out one with the direction using our right hand rules.0415

The diagram shows a proton, a positively charged particle moving with velocity V about to enter a uniform magnetic field directed in the page.0419

The axis are showing the fletching of the arrow, as if the arrow is going away from you.0428

The magnetic field is going into the plane of the page of the screen.0433

As the proton moves in the magnetic field, determine the direction of the force on the proton.0439

We are going to use our right hand rule.0443

Positive charge right hand, take you right hand and point the fingers of your right hand in the direction of the velocity.0446

From my perspective on the screen, I would point this way.0452

The magnetic field is directed into the page and my thumb is going to point in the direction of the force, which for me is toward the top of the screen.0455

If you do the same thing, you should come up also with a force that pointing0464

toward the top of your screen or the page, depending on how you are looking at this.0468

By the right hand rule, we know that the magnetic force on our charged particle is up.0472

Note that it is perpendicular to the velocity and perpendicular to the magnetic field again.0480

The magnetic force cannot perform work on a moving charge but it can change the charges direction because it always operate perpendicular to the objects velocity.0488

It can move it in a circle of the magnetic force is constant.0498

Here we have a positively charged particle moving with some velocity V, in the uniform magnetic field that is coming out of the plane of the screen.0501

The force on that by the right hand rule, as I do my V × B is toward the center of the circle.0510

That is going to provide the centripetal force to allow this object to move in a circular path.0516

We can even look at this in a little bit more detail.0522

We know the magnitude of that magnetic force is Q VB sin θ.0524

The magnetic force in this case must be providing our centripetal force, since the angle between V and B is 90°, sin θ is going to be 1.0529

That implies then that the magnetic force Q VB is equal to our centripetal force, MV²/ radius .0540

We can solve for the radius equal to MV/ QB.0550

It was kind of cool here, note that MV that is the momentum of our particle.0558

You can change the radius by changing strength of the magnetic field.0573

We have talked about the magnetic force on a moving charge particle.0581

We talked about the electrical force, the Coulombic force on a charge particle.0584

You have to deal with both of these at the same time.0588

The electric field can do work on a moving charge.0591

Remember the magnetic field cannot do work on a moving charge.0594

But when you put all this together, you get what we call the Lorentz force, the total electromagnetic force on a charge particle.0596

And that is going to be the electric field component QE, there is our electric or Coulombic piece + V × B which is QV × B.0603

There is our magnetic contribution to the total force on a moving charged particle.0619

The velocity selector is a very interesting tool.0634

A charged particle in ×, the electric and magnetic fields can undergo constant velocity motion if the velocity, the magnetic field, and the electric field, are all selected perpendicular to each other.0637

If you set the velocity equal to the electric field strength ÷ the magnetic field strength,0649

the particle can travel through the selector without any deflection whatsoever.0655

Particles with any other velocity are diverted off to the sides.0659

You put a bunch of charged particles into this machine, the only ones that are going to make it all the way out0663

are those that have the exact velocity that you are after, equal to the electric field strength ÷ the magnetic field strength.0669

Let us take a look at this analytically for a second.0676

In order for this to happen, we had note that the electric field moving up on our particle0678

must absolutely balance the magnetic field, the force pulling it toward the opposite direction down.0684

The electric force must equal the magnetic force which implies that QE must be equal to QV × B.0690

Or looking at magnitudes, QE must equal Q VB.0708

We gave it the sin θ piece because the angle between V and B is going to be 90°,0714

which implies then that the velocity that makes it through here, diverted where the electric force and0719

the magnetic force are absolutely balanced is just going to be E/ V.0725

Anything that is different is going to be off in the direction, it is not going to make it through your machine.0730

This is a very popular type question on AP tests.0735

Let us take a look at mass spectrometer, another tool that uses the magnetic force.0742

Magnetic fields accelerate moving charges so that they travel in a circle, in a uniform magnetic field.0747

You can use that to determine the mass of an unknown particle.0752

You ever charged unknown particle coming in here, we do not know its mass, we can use the magnetic field to apply a force, a centripetal force to spin it.0755

Depending on where we detect it here, we can determine what its mass is.0764

The further away it is, the more mass it has.0769

The closer it is, the smaller the mass with that constant force.0772

You can use this in order to determine what sort of masses you have in an unknown conglomeration of materials.0775

As long as you can charge and accelerate them, you can then read where they hit here in order to determine their mass.0783

A very popular tool.0789

Let us take a look at a couple more examples starting with the velocity of the charged particle.0792

Let us say we have a particle with a charge of 6.4 × 10 ⁻19 C experiences a force of 2 × 10 ⁻12 N,0797

traveling through a 3 tesla magnetic field and angle of 30° to the field.0805

What is the particle’s velocity?0810

We will start by writing down our givens.0814

Our charge 6.4 × 10 ⁻19 C, our force 2 × 10 ⁻12 N, our magnetic field strength is 3 tesla, and our angle is 30°.0814

To find the magnetic force that is going to be Q VB sin θ.0835

But we are actually after the particles velocity.0845

As we are rearranging to find the velocity that is going to be the magnetic force ÷ QB sin θ.0848

Now I can substitute in my values.0860

This implies then that our velocity is going to be, we have the force of 2 × 10 ⁻12 N ÷ our charge 6.4 ×0863

10 ⁻19 C × our magnetic field strength 3 tesla × the sin of our angle 30°.0875

I come up with the velocity of about 2.08 × 10⁶ m/ s, 2,000,000 m/ s.0884

That particle is moving pretty quick.0898

Force on a moving charge.0903

We have a charge of 5 µc moving with the velocity of 5,000,000 m / s in the X direction.0904

Find the force on the charge due to a magnetic field of ½ tesla in the positive Y direction.0912

Let us start with our givens and finds.0920

We know our charge is 5 µc or 5 × 10⁻⁶ C.0922

Our velocity is 5,000,00 5 × 10⁶ m / s in the X direction.0929

I'm just going to write that in unit vector notation I ̂.0936

Our magnetic field strength is 0.5 tesla in the positive Y direction which should be J ̂.0941

To find our magnetic force that is going to be Q V × B or looking at magnitudes Q VB sin θ.0949

But in this problem it is pretty easy to see that they are perpendicular, θ = 90°.0964

Sin θ is going to equal 1.0971

Therefore, our magnetic force is going to be Q VB which is our charge 5 × 10⁻⁶ C × our velocity 5 × 10⁶ m / s × ½ tesla, or 12.5 N.0976

Let us do another example.1003

An electron is projected with an initial velocity of 50,000 m / s parallel to a uniform magnetic field of 25 tesla.1006

What is the resulting force on the electron?1015

You could go through a lot of math here but there is a key word that simplifies this problem tremendously.1018

The velocity is parallel to that uniform magnetic field.1024

If they are parallel, there is not going to be any force.1029

0 N is on the electron, they have to be perpendicular.1034

If you have our sin factor, sin 0 is going to be 0.1039

Your force is going to 0.1044

Because it is parallel, no force on the electron.1046

Example 6, for each of the diagrams below, indicate the direction of the magnetic force on the charged particle.1054

Over here, we have an electron going through a magnetic field between a couple of magnets here.1061

The first thing I think I'm going to do is draw in the direction of the magnetic field.1067

Magnetic fields run from north to south so let us draw those in first.1071

We got a negatively charged particle so I'm going to use a left hand rule, instead of the right hand rule.1076

I’m going to point the fingers of my left hand in the direction that particle is moving.1082

Curl my fingers in the direction of the magnetic field which we just drew in here.1087

And when I do that, I find that I get a magnetic force which is into the plane of the page or the plane in the screen.1092

There is my magnetic force by the left hand rule because it is a negative charge.1101

Let us come over here now and do it for a positive charge.1107

It means we can use our right hand rule.1110

You have a positive charge, its velocity is moving up.1112

Let us label that V.1116

Our magnetic field is into the plane of the screen so right hand rule point the fingers of my right hand in the direction the particle is moving.1119

Bend them in the direction of the magnetic field and my thumb is going to point in the direction of the force on those,1126

which from my perspective is going to be toward the left of the screen again.1133

To the left of the screen for this problem, applications of the right hand rule.1139

We call them right hand rule, even though you use the left for the negative charges.1145

Another example here.1152

An electron is released from rest between the poles of 2 bar magnets in a region where the magnitude of the magnetic field strength is 6 tesla as shown below.1153

What is the magnetic force on the electron?1162

Keywords here are, it is at rest.1166

As long as it is at rest, there is no magnetic force on that charged particle.1170

It has to be moving, in order to have that magnetic force.1176

The magnetic force is going to be 0 because the velocity is 0.1180

It is not moving, the only thing you can have on is an electrical force.1184

Let us take the example of a proton in orbit.1191

We have a proton moving in a circular orbit of radius ½ m perpendicular to a uniform magnetic field of magnitude 0.3 tesla.1194

Find the period and frequency of the proton’s orbit, as well as its speed.1203

A little more involved here.1207

Let us draw a picture of this to begin with.1209

There is a nice little happy proton orbit, our radius is 0.5 m.1213

As it is going around here at that point, it has an instantaneous velocity in that direction.1220

And we have a magnetic field of magnitude 0.3 tesla.1226

Find the period and frequency of the proton’s orbit as well as its speed.1239

I think where we are going to start here is, let us take a look at how it is moving in a circle.1244

We will use that equation we did before where we said the centripetal force has to be equal to the magnetic force,1251

because the magnetic force is what is causing that centripetal force.1258

The magnetic force is the centripetal force, causing it to move in a circle.1261

Centripetal force which is MV²/ R is equal to the magnitude of the magnetic force Q VB.1266

And sin θ we do not need because θ is 90° again, they are perpendicular, sin 90 is 1.1275

Rearranging here, we can take V²/ V here is going to be Q RB/ M.1284

That will simplify nicely.1294

This implies then that the left hand side, our velocity is going to be Q RB/ M.1296

Our Q we said, it is a proton, it must be 1.6 × 10 ⁻19 C.1300

Our radius is ½ m, our magnetic field strength is 0.3 tesla, and we have to divide it by the mass of our particle.1308

The mass of the proton you can look up, it is 1.67 × 10 ⁻27 kg.1320

Putting all that in my calculator, I come up with 1.44 × 10⁷ m/ s.1329

We have found its speed, we are after period and frequency.1347

First thing I'm going to do I think, is find out how long it takes to go once around the circle.1352

Once I have that, that is really going to be its period.1356

I can use the straightforward V = D/ T, because it is moving at a constant velocity,1359

which means that the time it takes is going to be distance it travels ÷ its velocity.1368

The distance it travels is its circumference 2 π R or 2 π × 0.5 m.1373

We just found its velocity as 1.44 × 10⁷ m / s.1380

The time it takes to go once around is right around 2.18 × 10⁻⁷ s, which is its period because period is the time it takes to go once around the circle.1386

How about frequency?1405

Frequency is just the reciprocal of period which is going to be 1/ 2.18 × 10⁻⁷ s, which is about 4.58 × 10⁶ Hz or 4.58 MHz.1407

Proton in orbit, let us do a velocity selector question.1437

Find the speed of a charged particle which passes through a velocity selector1444

with magnetic field strength of 1 tesla perpendicular to an electric field of 600,000 N/ C.1447

I remember the trick in the velocity selector is the electric force and the magnetic force has to balance.1456

The electric force must equal the magnetic force.1462

They have to have the same magnitude at opposite directions, of course, which implies that QE,1467

the magnitude of the electric force must equal the magnitude of the magnetic force Q VB and sin θ again.1472

Θ is going to be 90°, sin 90 is 1.1479

Therefore, the velocity is just going to be E/ B which will be 600,000 N/ C ÷ 1 tesla,1482

which implies then that our velocity is going to be 600,000 m/ s.1500

Particle with exactly that velocity is going to make it through that particle selector unhindered.1511

Let us do one last question, maybe with a couple of parts in a mass spectrometer.1517

We have a proton that is accelerated through a potential differences V before passing into a region of1524

uniform magnetic field into the plane of the screen as shown here.1529

Find the voltage necessary to give the proton a speed v as it enters the magnetic field region in terms of its mass, its velocity, and its charge Q.1534

Let us see, in order to start this, the energy that it has is the work that we do on it, which is going to be the charge × the potential difference.1545

Work, which is QV, is going to be manifested, it is going to be its kinetic energy as it goes into the mass spectrometer.1555

That is ½ MV², C v.1564

Voltage and speed, you got to be careful of these two.1569

Which implies then, solving for the voltage, the potential difference is going to be M × velocity²/ 2Q.1572

That part was not too bad.1586

Let us take a little bit further and determine the expression for the radius of the proton’s motion in the uniform magnetic field region.1589

The magnetic force on it is Q VB and that has to equal MV²/ R because it is moving in a circular path,1601

which implies that R is going to be equal to MV²/ Q VB, which is equal to MV/ QB, when we cancel out one of those velocity factors.1611

Radius in the uniform magnetic field MV/ QB.1627

Taking another step, sketch the path of the proton in the magnetic field.1635

Let us see, it is a positively charged particle so this looks like your right hand rule problem.1641

Point your fingers in the direction that it is moving, to the right of the screen as it enters the magnetic field.1647

Curl your fingers into the screen, in the direction of the magnetic field, and you are going to see that initially you have a force up.1653

As that moves, that is going to turn it.1661

You are going to get this curving path so it travels something like that.1663

You are going to see a circular path in that direction.1671

Last one, an electric field is applied in the same region as the uniform magnetic field to over here.1677

Determine the magnitude and direction of electric field required so that the proton passes through the region in a straight line.1684

Now we are setting this up so that we have a velocity selector, so that the particle goes through unhindered.1690

The first thing is, we saw the magnetic field.1698

The magnetic force is pointed toward the top of our screen, that means that our electric force is going to have to be down.1701

Therefore, our electric field is going to have to point down because it is a positive particle.1710

In the velocity selector, we have the electric force equal to the magnetic force, which implies that QE = Q VB,1716

which implies that the electric field strength has to be equal to V × B.1728

Hopefully, that gets you a good start on moving charges in magnetic fields.1739

Thank you for watching www.educator.com.1744

Make it a great day everyone.1747

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