Gauss's Law, AP Physics C/Electricity and Magnetism

Gauss's Law

I. Electricity: Lecture 5 | 87:00 min

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Gauss's Law

Electric Flux: If a uniform electric field E is perpendicular to a plane of area A, then the electric flux through the area is defined as the product EA. If E makes an angle theta with the normal (perpendicular) to the plane, then the flux is given by EAcos(theta).
In general, given an electric field E in a certain region of space, and a closed surface, we define the electric flux through the closed surface as a surface integral of the dot product of E and da, where da is a vector with a magnitude equal to the area of the surface element da and whose direction is the outward normal to the surface element da, and E is the electric field at the position of the element da.
Gauss’s law: The electric flux through any closed surface is equal to Q_enc / epsilon_0, where Q_enc is the charge enclosed within the closed surface, and epsilon_0 = 8.854 x 10^-12 in SI units.

Gauss's Law

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I. Electricity
	Electric Force	56:18
	Coulomb's Law	87:18
	Electric Field	97:24
	Electric Field of a Continuous Charge Distribution	100:12
	Gauss's Law	87:00
	Application of Gauss's Law, Part 1	66:48
	Application of Gauss's Law, Part 2	79:19
	Electric Potential, Part 1	86:57
	Electric Potential, Part 2	91:50
	Electric Potential, Part 3	69:12
	Electric Potential, Part 4	71:16
	Capacitor	84:14
	Combination of Capacitors	63:23
	Calculating Capacitance	55:14
	More on Filled Capacitors	77:13
	Electric Current	79:17
	Circuits	94:08
	Kirchhoff's Law	102:02
	RC Circuits	80:35
II. Magnetism
	Magnetic Field	98:19
	Magnetic Force on a Current Carrying Conductor	64:43
	Torque on a Current Carrying Loop	69:06
	Magnetic Field Produced By Current, Part 1	57:58
	Magnetic Field Produced By Current, Part 2	79:29
	Magnetic Field Produced By Current, Part 3	50:37
	Faraday's Law	70:38
	Motional EMF	60:17
	Induced Electric Field	65:19
	Inductance	71:10
	RL Circuits	85:19
	Circuit Oscillation	82:26
	Maxwell's Equations	72:35

AP Physics C: Electricity and Magnetism

I. Electricity
	Electric Force			56:18
		Intro		0:00
		Electric Charge		0:18
			Matter Consists of Atom	1:01
			Two Types of Particles: Protons & Neutrons	1:48
			Object with Excess Electrons: Negatively Charged	7:58
			Carbon Atom	8:30
			Positively Charged Object	9:55
		Electric Charge		10:07
			Rubber Rod Rubs Against Fur (Negative Charge)	10:16
			Glass Rod Rub Against Silk (Positive Charge)	11:48
			Hanging Rubber Rod	12:44
		Conductors and Insulators		16:00
			Electrons Close to Nucleus	18:34
			Conductors Have Mobile Charge	21:30
			Insulators: No Moving Electrons	23:06
			Copper Wire Connected to Excess Negative charge	23:22
			Other End Connected to Excess Positive Charge	24:09
		Charging a Metal Object		27:25
			By Contact	28:05
			Metal Sphere on an Insulating Stand	28:16
			Charging by Induction	30:59
			Negative Rubber Rod	31:26
			Size of Atom	36:08
		Extra Example 1: Three Metallic Objects		7:32
		Extra Example 2: Rubber Rod and Two Metal Spheres		6:25
	Coulomb's Law			87:18
		Intro		0:00
		Coulomb's Law		0:59
			Two Point Charges by Distance R	1:11
			Permitivity of Free Space	5:28
		Charges on the Vertices of a Triangle		8:00
			3 Charges on Vertices of Right Triangle	8:29
			Charge of 4, -5 and -2 micro-Coulombs	10:00
			Force Acting on Each Charge	10:58
		Charges on a Line		21:29
			2 Charges on X-Axis	22:40
			Where Should Q should be Placed, Net Force =0	23:23
		Two Small Spheres Attached to String		31:08
			Adding Some Charge	32:03
			Equilibrium Net Force on Each Sphere = 0	33:38
		Simple Harmonic Motion of Point Charge		37:40
			Two Charges on Y-Axis	37:55
			Charge is Attracted	39:52
			Magnitude of Net Force on Q	42:23
		Extra Example 1: Vertices of Triangle		9:39
		Extra Example 2: Tension in String		11:46
		Extra Example 3: Two Conducting Spheres		6:29
		Extra Example 4: Force on Charge		9:21
	Electric Field			97:24
		Intro		0:00
		Definition of Electric Field		0:11
			Q1 Produces Electric Field	3:23
			Charges on a Conductor	4:26
		Field of a Point Charge		13:10
			Charge Point Between Two Fields	13:20
			Electric Field E=kq/r2	14:29
			Direction of the Charge Field	15:10
			Positive Charge, Field is Radially Out	15:45
		Field of a Collection of a Point Charge		19:40
			Two Charges Q1,Q2	19:56
			Q1 Positive, Electric Field is Radially Out	20:32
			Q2 is Negative, Electric Field is Radially Inward	20:46
			4 Charges are Equal	23:54
		Parallel Plate Capacitor		25:42
			Two Plates ,Separated by a Distance	26:44
			Fringe Effect	30:26
			E=Constant Between the Parallel Plate Capacitor	30:40
		Electric Field Lines		35:16
			Pictorial Representation of Electric Field	35:30
			Electric Lines are Tangent to the Vector	35:57
			Lines Start at Positive Charge, End on Negative Charge	41:24
			Parallel Line Proportional to Charge	45:51
			Lines Never Cross	46:00
		Conductors and Shielding		49:33
			Static Equilibrium	51:09
			No Net Moment of Charge	53:09
			Electric Field is Perpendicular to the Surface of Conductor	55:40
		Extra Example 1: Plastic Sphere Between Capacitor		8:46
		Extra Example 2: Electron Between Capacitor		11:52
		Extra Example 3: Zero Electric Field		10:44
		Extra Example 4: Dimensional Analysis		6:01
	Electric Field of a Continuous Charge Distribution			100:12
		Intro		0:00
		General Expression For E		0:16
			Magnitude of Electric Field	1:29
			Disk: Spread Charge Distribution	5:04
			Volume Contains Charges	6:16
		Charged Rod One Dimension		16:28
			Rod in X-Axis	17:00
			Charge Density	17:49
			Find Electric Field at Distance 'A'	19:05
		Charged Rod, Cont.		32:48
			Origin at Center, Extends From -L to +L	33:11
			Dividing Rod into Pieces	34:50
			Electric Field Produced At Point P	35:09
			Another Element	37:43
			'Y' Components of Electric Field	42:15
		Charged Ring		54:23
			Find Electric Field Above the Center	54:48
		Charged Disc		58:43
			Collection of Rings	59:10
		Example 1: Charged Disk		17:18
		Example 2: Semicircle with Charge		7:49
		Example 3: Charged Cylindrical Charge		13:53
	Gauss's Law			87:00
		Intro		0:00
		Electric Field Lines		0:11
			Magnitude of Field	2:04
			Unit Area and Unit Lines	2:59
			Number of Lines Passing Through the Unit	6:45
		Electic Flux: Constant E		6:51
			Field Lines Equally Spaced	7:10
			Area Perpendicular To Field Lines	7:46
			Electric Flux	8:36
			Area Perpendicular to Electric Lines	9:43
			Tilt the Area	10:58
			Flux of E Through Area	17:30
		Electric Flux: General Case		20:46
			Perpendicular at Different Directions	23:24
			Electric Field Given On a Patch	27:10
			Magnitude of Field	28:53
			Direction is Outward Normal	29:34
			Flux Through Patch	30:36
		Example		36:09
			Electric Field in Whole Space	37:16
			Sphere of Radius 'r'	37:30
			Flux Through Sphere	38:09
		Gauss's Law: Charge Outside		46:02
			Flux Through Radius Phase is Zero	50:09
			Outward normal 'n'	54:55
		Gauss's Law: Charge Enclosed		60:30
			Drawing Cones	60:51
		Example 1: Flux Through Square		7:08
		Example 2: Flux Through Cube		10:23
		Example 3: Flux Through Pyramid		5:01
	Application of Gauss's Law, Part 1			66:48
		Intro		0:00
		When is Gauss Law Useful?		0:18
			Need a Surface S	5:14
			Gaussian Surface	5:50
		Sphere of Charge		10:11
			Charge Density is Uniform	10:30
			Radius as 'A'	11:23
			Case 1: R>A	11:58
			Any Direction On Cone Is Same	20:28
			Case 2: R<A	25:15
			Point R Within the Surface	25:30
		Concentric Cavity		31:11
			Inside Circle and Outside Circle	31:48
			R>A	32:17
			R<B	36:40
		Radius Dependent Charge Density		37:39
			Sphere	38:09
			Total Charge: Q	39:46
			Spherical Shell	40:13
			Finding Electric Field R>A	42:36
			R<A	44:14
		Example 1: Charged Sphere		9:56
		Example 2: Charged Spherical Cavity		11:06
	Application of Gauss's Law, Part 2			79:19
		Intro		0:00
		Infinitely Long Line of Charge		0:13
			All Points Same Magnitude	5:02
			E is Perpendicular to Line	9:08
			Gauss's Law Cannot be Applied to Finite Length	15:50
		Infinitely Long Cylinder Of Charge		16:05
			Draw a Cylinder of Radius 'R'	16:36
			Line of Charge Along the Center	18:25
			R<A	18:39
			Electric Field of Special Direction	19:06
		Infinite Sheet of Charge		25:12
			Electric Field Above the Sheet	25:38
			Point is Above Height, Cylinder Intersects	26:29
			Curved Path	33:12
		Parallel Plate Capacitors		37:16
			Electric Field Between Sheets	39:16
		Conductors		41:55
			Adding Charge to Conductors	42:16
			In Electrostatic Equilibrium Charges Stop Moving	44:37
			Electric Field is Perpendicular to Surface	47:16
			Excess Charge Must Reside on Surface	47:38
		Example 1: Cylindrical Shell		7:45
		Example 2: Wire Surrounded by Shell		6:43
		Example 3: Sphere Surrounded by Spherical Shell		7:30
	Electric Potential, Part 1			86:57
		Intro		0:00
		Potential Difference Between Two Points		0:16
			Electric Field in Space By Stationary Charges	0:30
			Point Charge Moves From A to B	1:37
			Electric Field Exerts a Force	1:50
			Electric Potential Energy	5:34
			Work Done By External Agent	20:03
			Change in Potential Energy is Equal to Amount of Work Done	24:06
		Potential Difference in Uniform Electric Field		27:59
			Constant Electric Field	28:22
			Equipotential	40:22
		Parallel Plates		40:52
			Electric Field is Perpendicular to Plate	42:07
			Charge Released at A from Rest	49:00
		Motion of Charged Particle in a Uniform Electric Field		51:55
		Example 1: Work by Moving Electrons		3:45
		Example 2: Block and Spring		13:52
		Example 3: Particle on String		11:27
	Electric Potential, Part 2			91:50
		Intro		0:00
		Potential of a Point Charge		0:32
			Potential Difference Between A to B	1:25
			Draw a Circle	9:12
			Tangential to Sphere	9:33
			Moving Normally From Sphere	12:33
		Potential Energy of a Collection of Charges		26:33
			Potential Energy of Two Charges	26:44
			Work Done in Assembling the Configuration	27:29
			Bringing From Infinity to New Location	33:57
			Work Done by External Agent	36:22
			Potential Energy of the System	39:39
			Potential Energy for Two Charges	40:00
		Example		44:49
			Two Charges	45:03
			Speed at Infinity	48:01
		Electric Field from the Potential		51:12
			Finding E if V is Given	51:33
		Electric Dipole		56:22
			Two Equal and Opposite Charges Separated By a Distance	56:32
			If a << r1 or r2	60:23
		Example 1: Two Point Charges		17:56
		Example 2: Two Insulating Spheres		7:31
		Example 3: Electric Potential of Space		4:01
	Electric Potential, Part 3			69:12
		Intro		0:00
			Continuous Charge Distribution	0:27
			Finding Potential for a Charge Point	1:39
			Potential Produced at P	4:42
		Charged Ring		8:38
			Electric Field at Some Point of Axis	9:13
		Charged Disk		19:32
			Collection of Ring	20:40
			Finding Potential Point Above the Ring	22:19
			Potential Due to The Ring	23:40
		Finite Line of Charge		35:56
			Line of Change Along the X-Axis and Y-axis	36:11
		Example 1: Charged Rod		8:52
		Example 2: Bent Semicircle		4:48
		Example 3: Bent Semicircle with Variables		4:52
	Electric Potential, Part 4			71:16
		Intro		0:00
		Charged Conductors		0:12
			Adding Excess Charge to a Conductor	1:02
			E=0 Inside Conductors	1:50
			Excess Charges Must Reside on Surface	3:40
			E Normal on the Surface	9:31
			Surface of Conductor is Equipotential	11:59
		Conducting Sphere		19:28
			Adding Charge to the Sphere	19:41
			Electric Field Outside is Concentrated at Center	20:05
			Electric Potential is Same as Center	23:01
		Example		26:24
			Two Spheres with Distance and of Different Size	26:45
			Connecting Both Spheres with Conducting Wire	27:22
		Cavity Within a Conductor		39:43
			Hollow Conductor	40:19
			Electric Static Equilibrium	41:13
			Electric Field is Zero Within Cavity	53:20
		Example 1: Neutral Conducting Sphere		4:03
		Example 2: Conducting Sphere with Spherical Shell		13:45
	Capacitor			84:14
		Intro		0:00
		Capacitance		0:09
			Consider Two Conductor s	0:25
			Electric Field Passing from Positive to Negative	1:19
			Potential Difference	3:31
			Defining Capacitance	3:51
		Parallel Plate Capacitance		8:30
			Two Metallic Plates of Area 'a' and Distance 'd'	8:46
			Potential Difference between Plates	13:12
		Capacitance with a Dielectric		22:14
			Applying Electric Field to a Capacitor	22:44
			Dielectric	30:32
		Example		34:56
			Empty Capacitor	35:12
			Connecting Capacitor to a Battery	35:26
			Inserting Dielectric Between Plates	39:02
		Energy of a Charged Capacitor		43:01
			Work Done in Moving a Charge, Difference in Potential	47:48
		Example		54:10
			Parallel Plate Capacitor	54:22
			Connect and Disconnect the Battery	55:27
			Calculating Q=cv	55:50
			Withdraw Mica Sheet	56:49
			Word Done in Withdrawing the Mica	60:23
		Extra Example 1: Parallel Plate Capacitor		8:41
		Extra Example 2: Mica Dielectric		15:01
	Combination of Capacitors			63:23
		Intro		0:00
		Parallel Combination		0:20
			Two Capacitors in Parallel With a Battery	0:40
			Electric Field is Outside	5:47
			Point A is Directly Connected to Positive Terminal	7:57
			Point B is Directly Connected to Negative Terminal	8:10
			Voltage Across Capacitor	12:54
			Energy Stored	14:52
		Series Combination		17:58
			Two Capacitors Connected End to End With a Battery	18:10
			Equivalent Capacitor	25:20
			A is Same Potential	26:59
			C is Same Potential	27:06
			Potential Difference Across First Capacitor (Va-Vb)	27:42
			(Vb-Vc) is Potential Difference Across Second Capacitor	28:10
			Energy Stored in C1,C2	29:53
		Example		31:07
			Two Capacitor in Series, 2 in Parallel, 3 in Parallel, 1 Capacitor Connected	31:28
			Final Equivalent Circuit	37:31
		Extra Example 1: Four Capacitors		16:50
		Extra Example 2: Circuit with Switches		8:25
	Calculating Capacitance			55:14
		Intro		0:00
		Considering a Sphere		0:28
			Placing Charge on Sphere	2:14
			On the Surface of Sphere	4:12
		Spherical Capacitor		9:20
			Sphere of Radius a and Shell of Radius b	9:40
			Positive Charge on Outer Sphere	11:02
			Negative Charge on Inner Sphere	11:26
			Calculating Potential Difference	11:38
		Parallel Plate Capacitor		22:38
			Two Plates with Charges Positive and Negative	22:54
			Separation of Plate	25:10
		Cylindrical Capacitor		28:40
			Inner Cylinder and Outer Cylindrical Shell	29:01
			Linear Charge Density	30:41
		Example 1: Parallel Plate Capacitor		4:39
		Example 2: Spherical Capacitor		8:51
	More on Filled Capacitors			77:13
		Intro		0:00
		Electric Dipole is an Electric Field : Torque		0:13
			Magnitude of Dipole	1:15
			Starts to Rotate	5:38
			Force qe to the Right	5:59
			Finding the Torque	6:35
		Electric Dipole is an Electric Field : Potential Energy		13:56
			Electric Field Try's to Rotate	14:43
			Object on Center of Earth	16:04
			Applying Torque Equal and Opposite	17:05
		Water Molecule		25:43
			Carbon Molecules	31:39
			Net Dipole Moment is Zero	32:11
			Induced Dipole Moment	34:43
		Filled Capacitor		35:27
			Empty Capacitor with Charge on it	35:44
			Inserting a Dielectric	36:08
		Capacitor Partially Filled with Metallic Slab		44:33
			Capacitor with Slab of Distance 'd'	44:54
		Capacitor Partially Filled with a Dielectric Slab		51:59
			Change in Potential Difference	53:28
		Example 1: Parallel Plate Capacitor		13:37
		Example 2: Conducting Slab		8:20
	Electric Current			79:17
		Intro		0:00
		Definition		0:20
			Consider a Wire ,Cylindrical	0:40
			Cross Sectional Area	1:06
			Crossing Charges Will be Counted	2:50
			Amount of Charge Crosses Cross Sectional Area	3:29
			Current I=q/t	4:18
			Charges Flowing in Opposite Direction	5:58
			Current Density	6:19
			Applying Electric Field	11:50
		Current in a Wire		15:24
			Wire With a Cross Section Area 'A'	15:33
			Current Flowing to Right	18:57
			How Much Charge Crosses Area 'A'	19:15
			Drift Velocity	20:02
			Carriers in Cylinder	22:40
		Ohm's Law		24:58
			Va-Vb = Electric Field times Length of Wire	28:27
			Ohm's Law	28:54
			Consider a Copper Wire of 1m , Cross Sectional Area 1cm/sq	34:24
		Temperature Effect		37:07
			Heating a Wire	37:05
			Temperature Co-Efficient of Resistivity	39:57
		Battery EMF		43:00
			Connecting a Resistance to Battery	44:30
			Potential Difference at Terminal of Battery	45:15
		Power		53:30
			Battery Connected with a Resistance	53:47
			Work Done on Charge	56:55
			Energy Lost Per Second	60:35
		Extra Example 1: Current		9:46
		Extra Example 2: Water Heater		8:05
	Circuits			94:08
		Intro		0:00
		Simple Rules		0:16
			Resistance in Series	0:33
			Current Passing Per Second is Equal	1:36
			Potential Difference	3:10
			Parallel Circuit, R1, R2	5:08
			Battery, Current Starts From Positive Terminal to Negative Terminal	10:08
		Series Combination of Resistances		13:06
			R1, R2 Connected to Battery	13:35
			Va-Vb=Ir1,Vb-Vc=Ir2	16:59
			Three Resistance Connected in Series Req=r1+r2+r3	18:55
		Parallel Combination of Resistance		19:28
			R1 and R2 Combined Parallel	19:50
			I=i1+i2 (Total Current)	24:26
			Requ=I/E	24:51
		A Simple Circuit		27:57
			Current Splits	29:15
			Total Resistance	31:52
			Current I= 6/17.2	35:10
		Another Simple Circuit		37:46
			Battery has Small Internal Resistance	38:02
			2 Ohms Internal Resistance, and Two Resistance in Parallel	38:24
			Drawing Circuit	48:53
			Finding Current	52:06
		RC Circuit		55:17
			Battery , Resistance and Capacitance Connected	55:30
			Current is Function of Time	58:00
			R, C are Time Constants	59:25
		Extra Example 1: Resistor Current/Power		4:17
		Extra Example 2: Find Current		6:03
		Extra Example 3: Find Current		10:00
		Extra Example 4: Find Current		13:49
	Kirchhoff's Law			102:02
		Intro		0:00
		First Kirchhoff Rule		0:19
			Two Resistance Connected With a Battery	0:29
			Many Resistance	1:40
			Increase in Potential from A to B	4:46
			Charge Flowing from Higher Potential to Lower Potential	5:13
		Second Kirchhoff Rule		9:17
			Current Entering	9:27
			Total Current Arriving is Equal Current Leaving	13:20
		Example		14:10
			Battery 6 V, Resistance 20, 30 Ohms and Another Battery 4v	14:30
			Current Entering I2+I3	21:18
		Example 2		31:20
			2 Loop circuit with 6v and 12 v and Resistance, Find Current in Each Resistance	32:29
		Example 3		42:02
			Battery and Resistance in Loops	42:23
		Ammeters and Voltmeters		56:22
			Measuring Current is Introducing an Ammeter	56:35
			Connecting Voltmeter, High Resistance	57:31
		Extra Example 1: Find Current		18:47
		Extra Example 2: Find Current		13:35
		Extra Example 3: Find Current		10:23
	RC Circuits			80:35
		Intro		0:00
		Charging a Capacitor: Circuit Equation		0:09
			Circuit with a Resistance , Capacitance and a Battery	0:20
			Closing Switch at T=0	1:36
			Applying Kirchhoff's Rule	6:26
			Change in Potential is Zero	6:52
			Solution Tau dq/dt= ec-q	16:25
		Discharging a Capacitor		27:14
			Charged Capacitor Connect to Switch and Resistance	27:30
			Closing the Switch at T=0	28:11
		Example		36:50
			12V Battery with Switch and Resistance 10mili ohms and Capacitor Connected 10 Micro Farad	37:02
			Time Constant	38:58
			Charge at q=0 at t=1sec	40:16
		Example		42:58
			Switch With Capacitor and Resistance	43:31
			What Time Charge C Has Initial Valve	45:17
			How Long Charge Energy Stored in C to Drop Half of Initial Value	46:55
		Example 1: RC Circuit 1		6:49
		Example 2: RC Circuit 2		12:53
		Example 3: RC Circuit 3		10:42
II. Magnetism
	Magnetic Field			98:19
		Intro		0:00
		Magnets		0:13
			Compass Will Always Point North	3:49
			Moving a Compass Needle	5:50
		Force on a Charged Particles		10:37
			Electric Field and Charge Particle Q	10:48
			Charge is Positive Force	11:11
			Charge Particle is At Rest	13:38
			Taking a Charged Particle and Moving to Right	16:15
			Using Right Hand Rule	23:37
			C= Magnitude of A, B	26:30
			Magnitude of C	26:55
		Motion of Particle in Uniform Magnetic Field		33:30
			Magnetic Field has Same Direction	34:02
			Direction of Force	38:40
			Work Done By Force=0	41:40
			Force is Perpendicular With Velocity	42:00
		Bending an Electron Beam		48:09
			Heating a Filament	48:29
			Kinetic Energy of Battery	51:54
			Introducing Magnetic Field	52:10
		Velocity Selector		53:45
			Selecting Particles of Specific Velocity	54:00
			Parallel Plate Capacitor	54:30
			Magnetic Force	56:20
			Magnitude of Force	56:45
		Extra Example 1: Vectors		19:24
		Extra Example 2: Proton in Magnetic Field		8:33
		Extra Example 3: Proton Circular Path		10:46
	Magnetic Force on a Current Carrying Conductor			64:43
		Intro		0:00
		Current Carrying Conductor in a Magnetic Field		0:19
			Current Though the Wire Connected to Battery	1:22
			Current Exerts Force Toward the Left	2:16
			IF Current is Reversed ,Force Exerts on Right	2:47
		Magnetic Force		3:31
			Wire with Current 'I' and with magnetic Field	4:02
			Force Exerted by Magnetic field	5:05
			Applying right hand Rule	5:25
			Let N be Number of Charge Carries Per /Vol	6:40
			Force on Wire	8:30
			Number of Charge Crossing in Time 't'	12:51
		Example		22:32
			Wire Bent to Semi Circle and Rest is Straight	22:51
			Applying Constant Magnetic Field in 'y' Direction	23:24
			Force n Straight Segment	23:50
			Net Force	34:19
		Example 1: Rod on Rails		15:37
		Example 2: Magnetic Force on Wire		13:59
	Torque on a Current Carrying Loop			69:06
		Intro		0:00
		B-Field Parallel to Plane of the Loop		0:27
			Loop in the X-Y Plane	1:06
			Net Force on Loop	7:45
		B-Field Not Parallel to Plane of the Loop		15:16
			Loop in the X-Y Plane, Free to Rotate in X- Direction	15:32
			Force on Out of Page and Force in to the Page	15:59
			Loop Turns Through 90 Degrees	18:10
		Magnetic Moment		36:26
			Any Current Loop Has Current 'I'	36:51
			Electric Dipole in Electric Field	38:17
			Potential Energy	39:54
			Magnetic Potential Energy of Dipole	41:05
		Example		43:33
			Circular of Radius 'r' With Magnetic Field and Pass Current	43:42
			Torque	46:01
		Example 1: Loop in Magnetic Field		9:21
		Example 2: Rotating Charge		10:32
	Magnetic Field Produced By Current, Part 1			57:58
		Intro		0:00
		Biot-Savart Law		0:11
			Suppose A current Carrying Wire	0:50
			Magnetic Field Produced by the Tiny Element is Also Tiny	3:09
			Permeability of Free Space	4:56
		B-Field of a Straight Wire		8:40
			Wire in X Axis	9:05
			What is the Magnetic Field Produce at Point p	9:16
			Taking a Small Segment	9:57
			If Length is Infinite	26:26
		Semi Circular Wire		27:02
			Semicircular Wire of Radius 'R'	27:22
			Finding Magnetic Field at Center	27:48
		Circular Current in Loop		33:37
			Circular Loop with Current 'I'	33:47
			Current Above the Center	34:00
		Example 1: Loop Carrying Current		10:42
		Example 2: Concentric Loops		4:57
	Magnetic Field Produced By Current, Part 2			79:29
		Intro		0:00
		Ampere's Law		0:16
			Consider a Loop at Any Point in Loop	1:15
		Long Cylindrical Wire		9:08
			Wire of Radius 'r'	9:24
			Magnetic Field is Tangent to Circle and Has Same Magnitude	10:15
			B at r>R	21:58
			B at r<R	23:08
			B at r=R	25:49
		Toroid		26:58
			Wrap a Wire to Toroid	27:47
			Calculating the Magnetic Field for 1 Loop	29:30
		Solenoid		39:17
			Coil With Many Turns	39:35
			Each Loop Carrying Current	40:29
			Taking Loop Within the Solenoid and Close the Loop	43:05
			Applying Ampere's Law	43:33
		Example 1: Infinitely Long Wire		8:12
		Example 2: Straight Wire		4:15
		Example 3: Two Parallel Conductors		8:21
		Example 4: Solenoid		10:13
	Magnetic Field Produced By Current, Part 3			50:37
		Intro		0:00
		Magnetic Force Between Parallel Conductors		0:16
			Two Parallel Plate Capacitors with Current	0:40
			Magnetic Field by i1	1:50
			According to Right Hand Rule	2:37
		Example		10:20
			Wire of 4m Length	10:50
			Mass of Wire 1Kg	11:18
			Force of Repulsion =Mg	12:24
		Gauss's Law in Magnetism		15:36
			Surface of Area, Magnetic Field is Perpendicular to Surface	17:09
			Magnetic Flux Through Enclosed surface	19:23
		Example		26:44
			Magnetic Field Out of Page	27:54
			Consider a Flux Through Rectangular Loop	28:52
		Example 1: Two Parallel Wires		9:45
		Example 2: Cube with Magnetic Field		5:36
	Faraday's Law			70:38
		Intro		0:00
		Faraday's Law		0:14
			Coil Connected to Ammeter	0:29
			Introducing a Magnet	1:08
			Moving the Magnet Forward and Backward	1:33
			Flux Increasing in Time	2:20
			Induced Electro Motive Force EMF	4:20
			Iron Core Square with Battery and Switch, Ammeter	5:22
			Close the Switch, Current Appears	6:11
		Lenz's Law		9:17
			Wire with Current I and Wire Loop	9:30
			Magnetic Field is Into the Page	10:14
			Current Induced in Wire to Oppose Change in Flux	12:54
			Example: Two Wires with Resistance and Uniform Magnetic Field	16:00
		Increasing B		29:02
			Coil of 100 Turns	29:20
			B Perpendicular to Coil	30:47
			Flux Through Each Turn	32:25
		Rotating Coil		37:36
			Consider a Big Magnet and Rectangular Coil with many Turns	37:49
			Rotating Coil With Angular Velocity 'w'	41:49
		Example 1: Loop		9:51
		Example 2: Solenoid		6:57
		Example 3: Wrapped Square		7:16
	Motional EMF			60:17
		Intro		0:00
		Moving a Conducting Rod in Magnetic Field		0:24
			Rod Moving in a Plane with Velocity 'v'	0:49
			Charges Piles Up and Down Until Electric Force Balance 'B'	7:59
			Equilibrium	9:30
			Potential Difference, Distance to Length of Wire	9:59
		Rod Pulled By External Agent		11:30
			Resistance to Wire	12:01
			Introducing Uniform Magnetic Field into The page	12:14
			Finding Flux	14:45
			Power Delivered to Resistance	17:01
			Force Exerted by 'B' on Rod	19:10
			Power By Agent	22:26
		Sliding Rod		23:08
			Resistance with a Sliding Rod and Magnetic Field 'B'	23:35
			Push With Initial Velocity 'V0'	24:01
			Finding Current = I	25:20
		Rotating Rod		36:10
			Magnetic Field into The Page	36:19
			Rod fixed in Plane and Rotating	36:40
			Induced EMF in Segment	40:00
		Example 1: Bar in Magnetic Field		6:15
		Example 2: Rod in Magnetic Field		11:08
	Induced Electric Field			65:19
		Intro		0:00
		Change B to Induce E		0:54
			Loop with Magnetic Field B	1:10
			Flux is Positive With Choice of 'n'	2:45
			Suppose Magnetic Field is Changing	3:04
			B Changing with time Flux (>0)	3:24
			Change in Electric Field Induces magnetic Field	20:34
		Example		21:08
			Cylinder with Magnetic Field	21:20
			Fill With Radius 'r'	22:11
			Turn Off the Field	22:30
			Magnetic Flux Through Big Loop	29:59
		AC Generator		38:28
			Magnetic Field with Coil of Many Turns	38:50
			As the Coil Rotates Flux is Induced	39:18
			Coil Rotated by Angle	40:29
			Coil Connected to The Ring and End Connected to Lamp	42:12
			Kinetic Energy Strike the Coil and Rotating Coil will Produce Electric Energy	45:12
		Example 1: Electric Field		12:09
		Example 2: Electric Field		7:00
	Inductance			71:10
		Intro		0:00
		Mutual Inductance		0:10
			Two Coils	0:35
			Current is Time Dependent	0:54
			Flux Proportional	1:55
			Magnetic Flux in Coil 2	2:08
			Induced EMF	2:40
			Flux Through 2nd Coil Proportional to Current in First Coil	4:07
			Mutual Inductance	5:30
			Suppose Current is in 2nd Coil	9:28
		Example		12:15
			Two Coils M=0.001	12:26
			Φ= Mi1	14:17
			Induced EMF	15:44
		Example		18:30
			Solenoid with N turns	18:40
			B inside Solenoid	21:05
			Φ Through the Ring	22:14
		Self Inductance		27:50
			Single Coil with Current	28:33
			I with Time Dependent	28:54
			Φ Proportional to B , Proportional to I	30:00
			Induced EMF =-di/dt	31:27
		Example 1: Circular Wire		15:46
		Example 2: Two Coils		9:54
		Example 3: Coil		7:24
	RL Circuits			85:19
		Intro		0:00
		Current Raising		0:45
			Battery and Switch with Resistance and Inductance	1:17
			Close s1 at T=0	2:27
			With out Inductor , Current is E/R	4:03
			I at T=0	9:51
			Vb-Va= -Ir	15:05
			Log (i-e/r)	19:51
		Current Declining		27:16
			Resistance R and Inductance	27:37
			I= E/R	28:37
			Switch is On at T=0	29:10
		Example		39:46
			Battery and Resistance R Connected with Inductor	39:55
			Time Constant l/R	40:58
			Time to Reach Half Time	41:59
			per τ (1-1/e)	44:36
		Magnetic Energy		45:47
			E-IR-Ldi/dt	46:26
			Power Derived By Current	46:51
			Magnetic Energy Stored in Conductor	52:48
			U=Li2	55:28
		Magnetic Energy Density		57:49
			Solenoid	58:18
			U=1/2 Li2	59:03
			Energy Density	60:45
		Example 1: Circuit 1		6:13
		Example 2: Circuit 2		16:54
	Circuit Oscillation			82:26
		Intro		0:00
		Oscillation in LC Circuit: Qualitative Analysis		0:30
			Circuit with Capacitance and Inductance	1:27
		Comparison with a Spring Block System		4:57
			Close the Switch, Let the Block Move	5:51
			At V=0	7:06
		LC Circuit Oscillation :Quantitative Analysis		15:07
			U Total = Ue + U m	17:26
		Example RLC		29:25
			Battery =12V, Capacitor and Inductor	29:54
			Switch at B F> t	31:42
			Damped Oscillation	50:14
		Example 1: LC Circuit 1		7:34
		Example 2: LC Circuit 2		16:19
		Example 3: RLC Circuit		6:52
	Maxwell's Equations			72:35
		Intro		0:00
		Displacement Current		1:29
			Ampere's Law	3:04
			Surface Bounded by Path	3:48
			I Current Going Through Surface	4:53
			Charging a Capacitor	9:55
		Maxwell's Equation		18:26
			Integral Form	18:53
			E.da =Q/e0 in Closed Surface	18:55
			Absence of Magnetic Monopoles	19:55
			Flux Through the Surface Bounded By C	22:26
			Ampere's Law	23:01
		Plane Electromagnetic Wave		31:03
			Electric and Magnetic Field	31:27
		Example		39:20
			Electromagnetic Wave Traveling in X Direction	39:40
			Lamda=c/f	41:30
			B=E/C	43:49
		Energy and Momentum Carried by EM Waves		44:34
			Energy Density	46:35
			Area in Y-Z Plane , Wave in X -Direction	48:53
			Energy Crossing Per Unit Area	52:53
			Pointing Vector	53:11
			Reflection of Radioactive	60:26
		Example 1: Cylindrical Region		8:36
		Example 2: Electric Field of EM Wave		3:16

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Gauss's Law

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Gauss's Law

Gauss's Law

AP Physics C: Electricity and Magnetism