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Professor Jishi

Electric Field of a Continuous Charge Distribution

Slide Duration:Table of Contents

I. Electricity

Electric Force

56m 18s

- Intro0:00
- Electric Charge0:18
- Matter Consists of Atom1:01
- Two Types of Particles: Protons & Neutrons1:48
- Object with Excess Electrons: Negatively Charged7:58
- Carbon Atom8:30
- Positively Charged Object9:55
- Electric Charge10:07
- Rubber Rod Rubs Against Fur (Negative Charge)10:16
- Glass Rod Rub Against Silk (Positive Charge)11:48
- Hanging Rubber Rod12:44
- Conductors and Insulators16:00
- Electrons Close to Nucleus18:34
- Conductors Have Mobile Charge21:30
- Insulators: No Moving Electrons23:06
- Copper Wire Connected to Excess Negative charge23:22
- Other End Connected to Excess Positive Charge24:09
- Charging a Metal Object27:25
- By Contact28:05
- Metal Sphere on an Insulating Stand28:16
- Charging by Induction30:59
- Negative Rubber Rod31:26
- Size of Atom36:08
- Extra Example 1: Three Metallic Objects-1
- Extra Example 2: Rubber Rod and Two Metal Spheres-2

Coulomb's Law

1h 27m 18s

- Intro0:00
- Coulomb's Law0:59
- Two Point Charges by Distance R1:11
- Permitivity of Free Space5:28
- Charges on the Vertices of a Triangle8:00
- 3 Charges on Vertices of Right Triangle8:29
- Charge of 4, -5 and -2 micro-Coulombs10:00
- Force Acting on Each Charge10:58
- Charges on a Line21:29
- 2 Charges on X-Axis22:40
- Where Should Q should be Placed, Net Force =023:23
- Two Small Spheres Attached to String31:08
- Adding Some Charge32:03
- Equilibrium Net Force on Each Sphere = 033:38
- Simple Harmonic Motion of Point Charge37:40
- Two Charges on Y-Axis37:55
- Charge is Attracted39:52
- Magnitude of Net Force on Q42:23
- Extra Example 1: Vertices of Triangle-1
- Extra Example 2: Tension in String-2
- Extra Example 3: Two Conducting Spheres-3
- Extra Example 4: Force on Charge-4

Electric Field

1h 37m 24s

- Intro0:00
- Definition of Electric Field0:11
- Q1 Produces Electric Field3:23
- Charges on a Conductor4:26
- Field of a Point Charge13:10
- Charge Point Between Two Fields13:20
- Electric Field E=kq/r214:29
- Direction of the Charge Field15:10
- Positive Charge, Field is Radially Out15:45
- Field of a Collection of a Point Charge19:40
- Two Charges Q1,Q219:56
- Q1 Positive, Electric Field is Radially Out20:32
- Q2 is Negative, Electric Field is Radially Inward20:46
- 4 Charges are Equal23:54
- Parallel Plate Capacitor25:42
- Two Plates ,Separated by a Distance26:44
- Fringe Effect30:26
- E=Constant Between the Parallel Plate Capacitor30:40
- Electric Field Lines35:16
- Pictorial Representation of Electric Field35:30
- Electric Lines are Tangent to the Vector35:57
- Lines Start at Positive Charge, End on Negative Charge41:24
- Parallel Line Proportional to Charge45:51
- Lines Never Cross46:00
- Conductors and Shielding49:33
- Static Equilibrium51:09
- No Net Moment of Charge53:09
- Electric Field is Perpendicular to the Surface of Conductor55:40
- Extra Example 1: Plastic Sphere Between Capacitor-1
- Extra Example 2: Electron Between Capacitor-2
- Extra Example 3: Zero Electric Field-3
- Extra Example 4: Dimensional Analysis-4

Electric Field of a Continuous Charge Distribution

1h 40m 12s

- Intro0:00
- General Expression For E0:16
- Magnitude of Electric Field1:29
- Disk: Spread Charge Distribution5:04
- Volume Contains Charges6:16
- Charged Rod One Dimension16:28
- Rod in X-Axis17:00
- Charge Density17:49
- Find Electric Field at Distance 'A'19:05
- Charged Rod, Cont.32:48
- Origin at Center, Extends From -L to +L33:11
- Dividing Rod into Pieces34:50
- Electric Field Produced At Point P35:09
- Another Element37:43
- 'Y' Components of Electric Field42:15
- Charged Ring54:23
- Find Electric Field Above the Center54:48
- Charged Disc58:43
- Collection of Rings59:10
- Example 1: Charged Disk-1
- Example 2: Semicircle with Charge-2
- Example 3: Charged Cylindrical Charge-3

Gauss's Law

1h 27m

- Intro0:00
- Electric Field Lines0:11
- Magnitude of Field2:04
- Unit Area and Unit Lines2:59
- Number of Lines Passing Through the Unit6:45
- Electic Flux: Constant E6:51
- Field Lines Equally Spaced7:10
- Area Perpendicular To Field Lines7:46
- Electric Flux8:36
- Area Perpendicular to Electric Lines9:43
- Tilt the Area10:58
- Flux of E Through Area17:30
- Electric Flux: General Case20:46
- Perpendicular at Different Directions23:24
- Electric Field Given On a Patch27:10
- Magnitude of Field28:53
- Direction is Outward Normal29:34
- Flux Through Patch30:36
- Example36:09
- Electric Field in Whole Space37:16
- Sphere of Radius 'r'37:30
- Flux Through Sphere38:09
- Gauss's Law: Charge Outside46:02
- Flux Through Radius Phase is Zero50:09
- Outward normal 'n'54:55
- Gauss's Law: Charge Enclosed1:00:30
- Drawing Cones1:00:51
- Example 1: Flux Through Square-1
- Example 2: Flux Through Cube-2
- Example 3: Flux Through Pyramid-3

Application of Gauss's Law, Part 1

1h 6m 48s

- Intro0:00
- When is Gauss Law Useful?0:18
- Need a Surface S5:14
- Gaussian Surface5:50
- Sphere of Charge10:11
- Charge Density is Uniform10:30
- Radius as 'A'11:23
- Case 1: R>A11:58
- Any Direction On Cone Is Same20:28
- Case 2: R<A25:15
- Point R Within the Surface25:30
- Concentric Cavity31:11
- Inside Circle and Outside Circle31:48
- R>A32:17
- R<B36:40
- Radius Dependent Charge Density37:39
- Sphere38:09
- Total Charge: Q39:46
- Spherical Shell40:13
- Finding Electric Field R>A42:36
- R<A44:14
- Example 1: Charged Sphere-1
- Example 2: Charged Spherical Cavity-2

Application of Gauss's Law, Part 2

1h 19m 19s

- Intro0:00
- Infinitely Long Line of Charge0:13
- All Points Same Magnitude5:02
- E is Perpendicular to Line9:08
- Gauss's Law Cannot be Applied to Finite Length15:50
- Infinitely Long Cylinder Of Charge16:05
- Draw a Cylinder of Radius 'R'16:36
- Line of Charge Along the Center18:25
- R<A18:39
- Electric Field of Special Direction19:06
- Infinite Sheet of Charge25:12
- Electric Field Above the Sheet25:38
- Point is Above Height, Cylinder Intersects26:29
- Curved Path33:12
- Parallel Plate Capacitors37:16
- Electric Field Between Sheets39:16
- Conductors41:55
- Adding Charge to Conductors42:16
- In Electrostatic Equilibrium Charges Stop Moving44:37
- Electric Field is Perpendicular to Surface47:16
- Excess Charge Must Reside on Surface47:38
- Example 1: Cylindrical Shell-1
- Example 2: Wire Surrounded by Shell-2
- Example 3: Sphere Surrounded by Spherical Shell-3

Electric Potential, Part 1

1h 26m 57s

- Intro0:00
- Potential Difference Between Two Points0:16
- Electric Field in Space By Stationary Charges0:30
- Point Charge Moves From A to B1:37
- Electric Field Exerts a Force1:50
- Electric Potential Energy5:34
- Work Done By External Agent20:03
- Change in Potential Energy is Equal to Amount of Work Done24:06
- Potential Difference in Uniform Electric Field27:59
- Constant Electric Field28:22
- Equipotential40:22
- Parallel Plates40:52
- Electric Field is Perpendicular to Plate42:07
- Charge Released at A from Rest49:00
- Motion of Charged Particle in a Uniform Electric Field51:55
- Example 1: Work by Moving Electrons-1
- Example 2: Block and Spring-2
- Example 3: Particle on String-3

Electric Potential, Part 2

1h 31m 50s

- Intro0:00
- Potential of a Point Charge0:32
- Potential Difference Between A to B1:25
- Draw a Circle9:12
- Tangential to Sphere9:33
- Moving Normally From Sphere12:33
- Potential Energy of a Collection of Charges26:33
- Potential Energy of Two Charges26:44
- Work Done in Assembling the Configuration27:29
- Bringing From Infinity to New Location33:57
- Work Done by External Agent36:22
- Potential Energy of the System39:39
- Potential Energy for Two Charges40:00
- Example44:49
- Two Charges45:03
- Speed at Infinity48:01
- Electric Field from the Potential51:12
- Finding E if V is Given51:33
- Electric Dipole56:22
- Two Equal and Opposite Charges Separated By a Distance56:32
- If a << r1 or r21:00:23
- Example 1: Two Point Charges-1
- Example 2: Two Insulating Spheres-2
- Example 3: Electric Potential of Space-3

Electric Potential, Part 3

1h 9m 12s

- Intro0:00
- Continuous Charge Distribution0:27
- Finding Potential for a Charge Point1:39
- Potential Produced at P4:42
- Charged Ring8:38
- Electric Field at Some Point of Axis9:13
- Charged Disk19:32
- Collection of Ring20:40
- Finding Potential Point Above the Ring22:19
- Potential Due to The Ring23:40
- Finite Line of Charge35:56
- Line of Change Along the X-Axis and Y-axis36:11
- Example 1: Charged Rod-1
- Example 2: Bent Semicircle-2
- Example 3: Bent Semicircle with Variables-3

Electric Potential, Part 4

1h 11m 16s

- Intro0:00
- Charged Conductors0:12
- Adding Excess Charge to a Conductor1:02
- E=0 Inside Conductors1:50
- Excess Charges Must Reside on Surface3:40
- E Normal on the Surface9:31
- Surface of Conductor is Equipotential11:59
- Conducting Sphere19:28
- Adding Charge to the Sphere19:41
- Electric Field Outside is Concentrated at Center20:05
- Electric Potential is Same as Center23:01
- Example26:24
- Two Spheres with Distance and of Different Size26:45
- Connecting Both Spheres with Conducting Wire27:22
- Cavity Within a Conductor39:43
- Hollow Conductor40:19
- Electric Static Equilibrium41:13
- Electric Field is Zero Within Cavity53:20
- Example 1: Neutral Conducting Sphere-1
- Example 2: Conducting Sphere with Spherical Shell-2

Capacitor

1h 24m 14s

- Intro0:00
- Capacitance0:09
- Consider Two Conductor s0:25
- Electric Field Passing from Positive to Negative1:19
- Potential Difference3:31
- Defining Capacitance3:51
- Parallel Plate Capacitance8:30
- Two Metallic Plates of Area 'a' and Distance 'd'8:46
- Potential Difference between Plates13:12
- Capacitance with a Dielectric22:14
- Applying Electric Field to a Capacitor22:44
- Dielectric30:32
- Example34:56
- Empty Capacitor35:12
- Connecting Capacitor to a Battery35:26
- Inserting Dielectric Between Plates39:02
- Energy of a Charged Capacitor43:01
- Work Done in Moving a Charge, Difference in Potential47:48
- Example54:10
- Parallel Plate Capacitor54:22
- Connect and Disconnect the Battery55:27
- Calculating Q=cv55:50
- Withdraw Mica Sheet56:49
- Word Done in Withdrawing the Mica1:00:23
- Extra Example 1: Parallel Plate Capacitor-1
- Extra Example 2: Mica Dielectric-2

Combination of Capacitors

1h 3m 23s

- Intro0:00
- Parallel Combination0:20
- Two Capacitors in Parallel With a Battery0:40
- Electric Field is Outside5:47
- Point A is Directly Connected to Positive Terminal7:57
- Point B is Directly Connected to Negative Terminal8:10
- Voltage Across Capacitor12:54
- Energy Stored14:52
- Series Combination17:58
- Two Capacitors Connected End to End With a Battery18:10
- Equivalent Capacitor25:20
- A is Same Potential26:59
- C is Same Potential27:06
- Potential Difference Across First Capacitor (Va-Vb)27:42
- (Vb-Vc) is Potential Difference Across Second Capacitor28:10
- Energy Stored in C1,C229:53
- Example31:07
- Two Capacitor in Series, 2 in Parallel, 3 in Parallel, 1 Capacitor Connected31:28
- Final Equivalent Circuit37:31
- Extra Example 1: Four Capacitors-1
- Extra Example 2: Circuit with Switches-2

Calculating Capacitance

55m 14s

- Intro0:00
- Considering a Sphere0:28
- Placing Charge on Sphere2:14
- On the Surface of Sphere4:12
- Spherical Capacitor9:20
- Sphere of Radius a and Shell of Radius b9:40
- Positive Charge on Outer Sphere11:02
- Negative Charge on Inner Sphere11:26
- Calculating Potential Difference11:38
- Parallel Plate Capacitor22:38
- Two Plates with Charges Positive and Negative22:54
- Separation of Plate25:10
- Cylindrical Capacitor28:40
- Inner Cylinder and Outer Cylindrical Shell29:01
- Linear Charge Density30:41
- Example 1: Parallel Plate Capacitor-1
- Example 2: Spherical Capacitor-2

More on Filled Capacitors

1h 17m 13s

- Intro0:00
- Electric Dipole is an Electric Field : Torque0:13
- Magnitude of Dipole1:15
- Starts to Rotate5:38
- Force qe to the Right5:59
- Finding the Torque6:35
- Electric Dipole is an Electric Field : Potential Energy13:56
- Electric Field Try's to Rotate14:43
- Object on Center of Earth16:04
- Applying Torque Equal and Opposite17:05
- Water Molecule25:43
- Carbon Molecules31:39
- Net Dipole Moment is Zero32:11
- Induced Dipole Moment34:43
- Filled Capacitor35:27
- Empty Capacitor with Charge on it35:44
- Inserting a Dielectric36:08
- Capacitor Partially Filled with Metallic Slab44:33
- Capacitor with Slab of Distance 'd'44:54
- Capacitor Partially Filled with a Dielectric Slab51:59
- Change in Potential Difference53:28
- Example 1: Parallel Plate Capacitor-1
- Example 2: Conducting Slab-2

Electric Current

1h 19m 17s

- Intro0:00
- Definition0:20
- Consider a Wire ,Cylindrical0:40
- Cross Sectional Area1:06
- Crossing Charges Will be Counted2:50
- Amount of Charge Crosses Cross Sectional Area3:29
- Current I=q/t4:18
- Charges Flowing in Opposite Direction5:58
- Current Density6:19
- Applying Electric Field11:50
- Current in a Wire15:24
- Wire With a Cross Section Area 'A'15:33
- Current Flowing to Right18:57
- How Much Charge Crosses Area 'A'19:15
- Drift Velocity20:02
- Carriers in Cylinder22:40
- Ohm's Law24:58
- Va-Vb = Electric Field times Length of Wire28:27
- Ohm's Law28:54
- Consider a Copper Wire of 1m , Cross Sectional Area 1cm/sq34:24
- Temperature Effect37:07
- Heating a Wire37:05
- Temperature Co-Efficient of Resistivity39:57
- Battery EMF43:00
- Connecting a Resistance to Battery44:30
- Potential Difference at Terminal of Battery45:15
- Power53:30
- Battery Connected with a Resistance53:47
- Work Done on Charge56:55
- Energy Lost Per Second1:00:35
- Extra Example 1: Current-1
- Extra Example 2: Water Heater-2

Circuits

1h 34m 8s

- Intro0:00
- Simple Rules0:16
- Resistance in Series0:33
- Current Passing Per Second is Equal1:36
- Potential Difference3:10
- Parallel Circuit, R1, R25:08
- Battery, Current Starts From Positive Terminal to Negative Terminal10:08
- Series Combination of Resistances13:06
- R1, R2 Connected to Battery13:35
- Va-Vb=Ir1,Vb-Vc=Ir216:59
- Three Resistance Connected in Series Req=r1+r2+r318:55
- Parallel Combination of Resistance19:28
- R1 and R2 Combined Parallel19:50
- I=i1+i2 (Total Current)24:26
- Requ=I/E24:51
- A Simple Circuit27:57
- Current Splits29:15
- Total Resistance31:52
- Current I= 6/17.235:10
- Another Simple Circuit37:46
- Battery has Small Internal Resistance38:02
- 2 Ohms Internal Resistance, and Two Resistance in Parallel38:24
- Drawing Circuit48:53
- Finding Current52:06
- RC Circuit55:17
- Battery , Resistance and Capacitance Connected55:30
- Current is Function of Time58:00
- R, C are Time Constants59:25
- Extra Example 1: Resistor Current/Power-1
- Extra Example 2: Find Current-2
- Extra Example 3: Find Current-3
- Extra Example 4: Find Current-4

Kirchhoff's Law

1h 42m 2s

- Intro0:00
- First Kirchhoff Rule0:19
- Two Resistance Connected With a Battery0:29
- Many Resistance1:40
- Increase in Potential from A to B4:46
- Charge Flowing from Higher Potential to Lower Potential5:13
- Second Kirchhoff Rule9:17
- Current Entering9:27
- Total Current Arriving is Equal Current Leaving13:20
- Example14:10
- Battery 6 V, Resistance 20, 30 Ohms and Another Battery 4v14:30
- Current Entering I2+I321:18
- Example 231:20
- 2 Loop circuit with 6v and 12 v and Resistance, Find Current in Each Resistance32:29
- Example 342:02
- Battery and Resistance in Loops42:23
- Ammeters and Voltmeters56:22
- Measuring Current is Introducing an Ammeter56:35
- Connecting Voltmeter, High Resistance57:31
- Extra Example 1: Find Current-1
- Extra Example 2: Find Current-2
- Extra Example 3: Find Current-3

RC Circuits

1h 20m 35s

- Intro0:00
- Charging a Capacitor: Circuit Equation0:09
- Circuit with a Resistance , Capacitance and a Battery0:20
- Closing Switch at T=01:36
- Applying Kirchhoff's Rule6:26
- Change in Potential is Zero6:52
- Solution Tau dq/dt= ec-q16:25
- Discharging a Capacitor27:14
- Charged Capacitor Connect to Switch and Resistance27:30
- Closing the Switch at T=028:11
- Example36:50
- 12V Battery with Switch and Resistance 10mili ohms and Capacitor Connected 10 Micro Farad37:02
- Time Constant38:58
- Charge at q=0 at t=1sec40:16
- Example42:58
- Switch With Capacitor and Resistance43:31
- What Time Charge C Has Initial Valve45:17
- How Long Charge Energy Stored in C to Drop Half of Initial Value46:55
- Example 1: RC Circuit 1-1
- Example 2: RC Circuit 2-2
- Example 3: RC Circuit 3-3

II. Magnetism

Magnetic Field

1h 38m 19s

- Intro0:00
- Magnets0:13
- Compass Will Always Point North3:49
- Moving a Compass Needle5:50
- Force on a Charged Particles10:37
- Electric Field and Charge Particle Q10:48
- Charge is Positive Force11:11
- Charge Particle is At Rest13:38
- Taking a Charged Particle and Moving to Right16:15
- Using Right Hand Rule23:37
- C= Magnitude of A, B26:30
- Magnitude of C26:55
- Motion of Particle in Uniform Magnetic Field33:30
- Magnetic Field has Same Direction34:02
- Direction of Force38:40
- Work Done By Force=041:40
- Force is Perpendicular With Velocity42:00
- Bending an Electron Beam48:09
- Heating a Filament48:29
- Kinetic Energy of Battery51:54
- Introducing Magnetic Field52:10
- Velocity Selector53:45
- Selecting Particles of Specific Velocity54:00
- Parallel Plate Capacitor54:30
- Magnetic Force56:20
- Magnitude of Force56:45
- Extra Example 1: Vectors-1
- Extra Example 2: Proton in Magnetic Field-2
- Extra Example 3: Proton Circular Path-3

Magnetic Force on a Current Carrying Conductor

1h 4m 43s

- Intro0:00
- Current Carrying Conductor in a Magnetic Field0:19
- Current Though the Wire Connected to Battery1:22
- Current Exerts Force Toward the Left2:16
- IF Current is Reversed ,Force Exerts on Right2:47
- Magnetic Force3:31
- Wire with Current 'I' and with magnetic Field4:02
- Force Exerted by Magnetic field5:05
- Applying right hand Rule5:25
- Let N be Number of Charge Carries Per /Vol6:40
- Force on Wire8:30
- Number of Charge Crossing in Time 't'12:51
- Example22:32
- Wire Bent to Semi Circle and Rest is Straight22:51
- Applying Constant Magnetic Field in 'y' Direction23:24
- Force n Straight Segment23:50
- Net Force34:19
- Example 1: Rod on Rails-1
- Example 2: Magnetic Force on Wire-2

Torque on a Current Carrying Loop

1h 9m 6s

- Intro0:00
- B-Field Parallel to Plane of the Loop0:27
- Loop in the X-Y Plane1:06
- Net Force on Loop7:45
- B-Field Not Parallel to Plane of the Loop15:16
- Loop in the X-Y Plane, Free to Rotate in X- Direction15:32
- Force on Out of Page and Force in to the Page15:59
- Loop Turns Through 90 Degrees18:10
- Magnetic Moment36:26
- Any Current Loop Has Current 'I'36:51
- Electric Dipole in Electric Field38:17
- Potential Energy39:54
- Magnetic Potential Energy of Dipole41:05
- Example43:33
- Circular of Radius 'r' With Magnetic Field and Pass Current43:42
- Torque46:01
- Example 1: Loop in Magnetic Field-1
- Example 2: Rotating Charge-2

Magnetic Field Produced By Current, Part 1

57m 58s

- Intro0:00
- Biot-Savart Law0:11
- Suppose A current Carrying Wire0:50
- Magnetic Field Produced by the Tiny Element is Also Tiny3:09
- Permeability of Free Space4:56
- B-Field of a Straight Wire8:40
- Wire in X Axis9:05
- What is the Magnetic Field Produce at Point p9:16
- Taking a Small Segment9:57
- If Length is Infinite26:26
- Semi Circular Wire27:02
- Semicircular Wire of Radius 'R'27:22
- Finding Magnetic Field at Center27:48
- Circular Current in Loop33:37
- Circular Loop with Current 'I'33:47
- Current Above the Center34:00
- Example 1: Loop Carrying Current-1
- Example 2: Concentric Loops-2

Magnetic Field Produced By Current, Part 2

1h 19m 29s

- Intro0:00
- Ampere's Law0:16
- Consider a Loop at Any Point in Loop1:15
- Long Cylindrical Wire9:08
- Wire of Radius 'r'9:24
- Magnetic Field is Tangent to Circle and Has Same Magnitude10:15
- B at r>R21:58
- B at r<R23:08
- B at r=R25:49
- Toroid26:58
- Wrap a Wire to Toroid27:47
- Calculating the Magnetic Field for 1 Loop29:30
- Solenoid39:17
- Coil With Many Turns39:35
- Each Loop Carrying Current40:29
- Taking Loop Within the Solenoid and Close the Loop43:05
- Applying Ampere's Law43:33
- Example 1: Infinitely Long Wire-1
- Example 2: Straight Wire-2
- Example 3: Two Parallel Conductors-3
- Example 4: Solenoid-4

Magnetic Field Produced By Current, Part 3

50m 37s

- Intro0:00
- Magnetic Force Between Parallel Conductors0:16
- Two Parallel Plate Capacitors with Current0:40
- Magnetic Field by i11:50
- According to Right Hand Rule2:37
- Example10:20
- Wire of 4m Length10:50
- Mass of Wire 1Kg11:18
- Force of Repulsion =Mg12:24
- Gauss's Law in Magnetism15:36
- Surface of Area, Magnetic Field is Perpendicular to Surface17:09
- Magnetic Flux Through Enclosed surface19:23
- Example26:44
- Magnetic Field Out of Page27:54
- Consider a Flux Through Rectangular Loop28:52
- Example 1: Two Parallel Wires-1
- Example 2: Cube with Magnetic Field-2

Faraday's Law

1h 10m 38s

- Intro0:00
- Faraday's Law0:14
- Coil Connected to Ammeter0:29
- Introducing a Magnet1:08
- Moving the Magnet Forward and Backward1:33
- Flux Increasing in Time2:20
- Induced Electro Motive Force EMF4:20
- Iron Core Square with Battery and Switch, Ammeter5:22
- Close the Switch, Current Appears6:11
- Lenz's Law9:17
- Wire with Current I and Wire Loop9:30
- Magnetic Field is Into the Page10:14
- Current Induced in Wire to Oppose Change in Flux12:54
- Example: Two Wires with Resistance and Uniform Magnetic Field16:00
- Increasing B29:02
- Coil of 100 Turns29:20
- B Perpendicular to Coil30:47
- Flux Through Each Turn32:25
- Rotating Coil37:36
- Consider a Big Magnet and Rectangular Coil with many Turns37:49
- Rotating Coil With Angular Velocity 'w'41:49
- Example 1: Loop-1
- Example 2: Solenoid-2
- Example 3: Wrapped Square-3

Motional EMF

1h 17s

- Intro0:00
- Moving a Conducting Rod in Magnetic Field0:24
- Rod Moving in a Plane with Velocity 'v'0:49
- Charges Piles Up and Down Until Electric Force Balance 'B'7:59
- Equilibrium9:30
- Potential Difference, Distance to Length of Wire9:59
- Rod Pulled By External Agent11:30
- Resistance to Wire12:01
- Introducing Uniform Magnetic Field into The page12:14
- Finding Flux14:45
- Power Delivered to Resistance17:01
- Force Exerted by 'B' on Rod19:10
- Power By Agent22:26
- Sliding Rod23:08
- Resistance with a Sliding Rod and Magnetic Field 'B'23:35
- Push With Initial Velocity 'V0'24:01
- Finding Current = I25:20
- Rotating Rod36:10
- Magnetic Field into The Page36:19
- Rod fixed in Plane and Rotating36:40
- Induced EMF in Segment40:00
- Example 1: Bar in Magnetic Field-1
- Example 2: Rod in Magnetic Field-2

Induced Electric Field

1h 5m 19s

- Intro0:00
- Change B to Induce E0:54
- Loop with Magnetic Field B1:10
- Flux is Positive With Choice of 'n'2:45
- Suppose Magnetic Field is Changing3:04
- B Changing with time Flux (>0)3:24
- Change in Electric Field Induces magnetic Field20:34
- Example21:08
- Cylinder with Magnetic Field21:20
- Fill With Radius 'r'22:11
- Turn Off the Field22:30
- Magnetic Flux Through Big Loop29:59
- AC Generator38:28
- Magnetic Field with Coil of Many Turns38:50
- As the Coil Rotates Flux is Induced39:18
- Coil Rotated by Angle40:29
- Coil Connected to The Ring and End Connected to Lamp42:12
- Kinetic Energy Strike the Coil and Rotating Coil will Produce Electric Energy45:12
- Example 1: Electric Field-1
- Example 2: Electric Field-2

Inductance

1h 11m 10s

- Intro0:00
- Mutual Inductance0:10
- Two Coils0:35
- Current is Time Dependent0:54
- Flux Proportional1:55
- Magnetic Flux in Coil 22:08
- Induced EMF2:40
- Flux Through 2nd Coil Proportional to Current in First Coil4:07
- Mutual Inductance5:30
- Suppose Current is in 2nd Coil9:28
- Example12:15
- Two Coils M=0.00112:26
- Φ= Mi114:17
- Induced EMF15:44
- Example18:30
- Solenoid with N turns18:40
- B inside Solenoid21:05
- Φ Through the Ring22:14
- Self Inductance27:50
- Single Coil with Current28:33
- I with Time Dependent28:54
- Φ Proportional to B , Proportional to I30:00
- Induced EMF =-di/dt31:27
- Example 1: Circular Wire-1
- Example 2: Two Coils-2
- Example 3: Coil-3

RL Circuits

1h 25m 19s

- Intro0:00
- Current Raising0:45
- Battery and Switch with Resistance and Inductance1:17
- Close s1 at T=02:27
- With out Inductor , Current is E/R4:03
- I at T=09:51
- Vb-Va= -Ir15:05
- Log (i-e/r)19:51
- Current Declining27:16
- Resistance R and Inductance27:37
- I= E/R28:37
- Switch is On at T=029:10
- Example39:46
- Battery and Resistance R Connected with Inductor39:55
- Time Constant l/R40:58
- Time to Reach Half Time41:59
- per τ (1-1/e)44:36
- Magnetic Energy45:47
- E-IR-Ldi/dt46:26
- Power Derived By Current46:51
- Magnetic Energy Stored in Conductor52:48
- U=Li255:28
- Magnetic Energy Density57:49
- Solenoid58:18
- U=1/2 Li259:03
- Energy Density1:00:45
- Example 1: Circuit 1-1
- Example 2: Circuit 2-2

Circuit Oscillation

1h 22m 26s

- Intro0:00
- Oscillation in LC Circuit: Qualitative Analysis0:30
- Circuit with Capacitance and Inductance1:27
- Comparison with a Spring Block System4:57
- Close the Switch, Let the Block Move5:51
- At V=07:06
- LC Circuit Oscillation :Quantitative Analysis15:07
- U Total = Ue + U m17:26
- Example RLC29:25
- Battery =12V, Capacitor and Inductor29:54
- Switch at B F> t31:42
- Damped Oscillation50:14
- Example 1: LC Circuit 1-1
- Example 2: LC Circuit 2-2
- Example 3: RLC Circuit-3

Maxwell's Equations

1h 12m 35s

- Intro0:00
- Displacement Current1:29
- Ampere's Law3:04
- Surface Bounded by Path3:48
- I Current Going Through Surface4:53
- Charging a Capacitor9:55
- Maxwell's Equation18:26
- Integral Form18:53
- E.da =Q/e0 in Closed Surface18:55
- Absence of Magnetic Monopoles19:55
- Flux Through the Surface Bounded By C22:26
- Ampere's Law23:01
- Plane Electromagnetic Wave31:03
- Electric and Magnetic Field31:27
- Example39:20
- Electromagnetic Wave Traveling in X Direction39:40
- Lamda=c/f41:30
- B=E/C43:49
- Energy and Momentum Carried by EM Waves44:34
- Energy Density46:35
- Area in Y-Z Plane , Wave in X -Direction48:53
- Energy Crossing Per Unit Area52:53
- Pointing Vector53:11
- Reflection of Radioactive1:00:26
- Example 1: Cylindrical Region-1
- Example 2: Electric Field of EM Wave-2

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For more information, please see full course syllabus of AP Physics C/Electricity and Magnetism

For more information, please see full course syllabus of AP Physics C/Electricity and Magnetism

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1 answer

Last reply by: Kyle Kosic

Mon Apr 4, 2011 8:42 PM

Post by Kyle Kosic on April 4, 2011

When he has 1/a^2 * sin(theta), couldn't he replace sin(theta) with x/a?

0 answers

Post by Daniel Brook on February 21, 2011

The Y-component aspect of the continuous charge distribution at the perpendicular bisector was really hard to understand. All of the trigonometry became really confusing. Either a different method of solving would have been nice or a more in-depth explanation of the problem could have helped.