# AP Physics C/Electricity and Magnetism Electric Field of a Continuous Charge Distribution

Section 1: Electricity: Lecture 4 | 1:40:12 min

Charge really comes in discrete chunks, but often it is mathematically convenient to treat a set of charges as if they were like a continuous fluid spread throughout a region of space. For example, a charged metal ball will have charge spread nearly uniformly all over its surface, and in for most purposes it will make sense to ignore the fact that this uniformity is broken at the atomic level. The electric field made by such a continuous charge distribution is the sum of the fields created by every part of it.Charge really comes in discrete chunks, but often it is mathematically convenient to treat a set of charges as if they were like a continuous fluid spread throughout a region of space.

Professor Jishi

Electric Field of a Continuous Charge Distribution

Slide Duration:Table of Contents

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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.