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Dan Fullerton

Electric Potential & Electric Potential Energy

Slide Duration:Table of Contents

I. Electricity

Electric Charge & Coulomb's Law

30m 48s

- Intro0:00
- Objective0:15
- Electric Charges0:50
- Matter is Made Up of Atoms0:52
- Most Atoms are Neutral1:02
- Ions1:11
- Coulomb1:18
- Elementary Charge1:34
- Law of Conservation of Charge2:03
- Example 12:39
- Example 23:42
- Conductors and Insulators4:41
- Conductors Allow Electric Charges to Move Freely4:43
- Insulators Do Not Allow Electric Charges to Move Freely4:50
- Resistivity4:58
- Charging by Conduction5:32
- Conduction5:37
- Balloon Example5:40
- Charged Conductor6:14
- Example 36:28
- The Electroscope7:16
- Charging by Induction7:57
- Bring Positive Rod Near Electroscope8:08
- Ground the Electroscope8:27
- Sever Ground Path and Remove Positive Rod9:07
- Example 49:39
- Polarization and Electric Dipole Moment11:46
- Polarization11:54
- Electric Dipole Moment12:05
- Coulomb's Law12:38
- Electrostatic Force, Also Known as Coulombic Force12:48
- How Force of Attraction or Repulsion Determined12:55
- Formula13:08
- Coulomb's Law: Vector Form14:18
- Example 516:05
- Example 618:25
- Example 719:14
- Example 823:21

Electric Fields

1h 19m 22s

- Intro0:00
- Objectives0:09
- Electric Fields1:33
- Property of Space That Allows a Charged Object to Feel a Force1:40
- Detect the Presence of an Electric Field1:51
- Electric Field Strength Vector2:03
- Direction of the Electric Field Vector2:21
- Example 13:00
- Visualizing the Electric Field4:13
- Electric Field Lines4:56
- E Field Due to a Point Charge7:19
- Derived from the Definition of the Electric Field and Coulomb's Law7:24
- Finding the Electric Field Due to Multiple Point Charges8:37
- Comparing Electricity to Gravity8:51
- Force8:54
- Field Strength9:09
- Constant9:19
- Charge Units vs. Mass Units9:35
- Attracts vs. Repel9:44
- Example 210:06
- Example 317:25
- Example 424:29
- Example 525:23
- Charge Densities26:09
- Linear Charge Density26:26
- Surface Charge Density26:30
- Volume Charge Density26:47
- Example 627:26
- Example 737:07
- Example 850:13
- Example 954:01
- Example 101:03:10
- Example 111:13:58

Gauss's Law

52m 53s

- Intro0:00
- Objectives0:07
- Electric Flux1:16
- Amount of Electric Field Penetrating a Surface1:19
- Symbol1:23
- Point Charge Inside a Hollow Sphere4:31
- Place a Point Charge Inside a Hollow Sphere of Radius R4:39
- Determine the Flux Through the Sphere5:09
- Gauss's Law8:39
- Total Flux8:59
- Gauss's Law9:10
- Example 19:53
- Example 217:28
- Example 322:37
- Example 425:40
- Example 530:49
- Example 645:06

Electric Potential & Electric Potential Energy

1h 14m 3s

- Intro0:00
- Objectives0:08
- Electric Potential Energy0:58
- Gravitational Potential Energy1:02
- Electric Potential Energy1:11
- Electric Potential1:19
- Example 11:59
- Example 23:08
- The Electron-Volt4:02
- Electronvolt4:16
- 1 eV is the Amount of Work Done in Moving an Elementary Charge Through a Potential Difference of 1 Volt4:26
- Conversion Ratio4:41
- Example 34:52
- Equipotential Lines5:35
- Topographic Maps5:36
- Lines Connecting Points of Equal Electrical Potential5:47
- Always Cross Electrical Field Lines at Right Angles5:57
- Gradient of Potential Increases As Equipotential Lines Get Closer6:02
- Electric Field Points from High to Low Potential6:27
- Drawing Equipotential Lines6:49
- E Potential Energy Due to a Point Charge8:20
- Electric Force from Electric Potential Energy11:59
- E Potential Due to a Point Charge13:07
- Example 414:42
- Example 515:59
- Finding Electric Field From Electric Potential19:06
- Example 623:41
- Example 725:08
- Example 826:33
- Example 929:01
- Example 1031:26
- Example 1143:23
- Example 1251:51
- Example 1358:12

Electric Potential Due to Continuous Charge Distributions

1h 1m 28s

- Intro0:00
- Objectives0:10
- Potential Due to a Charged Ring0:27
- Potential Due to a Uniformly Charged Desk3:38
- Potential Due to a Spherical Shell of Charge11:21
- Potential Due to a Uniform Solid Sphere14:50
- Example 123:08
- Example 230:43
- Example 341:58
- Example 451:41

Conductors

20m 35s

- Intro0:00
- Objectives0:08
- Charges in a Conductor0:32
- Charge is Free to Move Until the0:36
- All Charge Resides at Surface2:18
- Field Lines are Perpendicular to Surface2:34
- Electric Field at the Surface of a Conductor3:04
- Looking at Just the Outer Surface3:08
- Large Electric Field Where You Have the Largest Charge Density3:59
- Hollow Conductors4:22
- Draw Hollow Conductor and Gaussian Surface4:36
- Applying Gaussian Law4:53
- Any Hollow Conductor Has Zero Electric Field in Its Interior5:24
- Faraday Cage5:35
- Electric Field and Potential Due to a Conducting Sphere6:03
- Example 17:31
- Example 212:39

Capacitors

41m 23s

- Intro0:00
- Objectives0:08
- What is a Capacitor?0:42
- Electric Device Used to Store Electrical Energy0:44
- Place Opposite Charges on Each Plate1:10
- Develop a Potential Difference Across the Plates1:14
- Energy is Stored in the Electric Field Between the Plates1:17
- Capacitance1:22
- Ratio of the Charge Separated on the Plates of a Capacitor to the Potential Difference Between the Plates1:25
- Units of Capacitance1:32
- Farad1:37
- Formula1:52
- Calculating Capacitance1:59
- Assume Charge on Each Conductor2:05
- Find the Electric Field2:11
- Calculate V by Integrating the Electric Field2:21
- Utilize C=Q/V to Solve for Capitance2:33
- Example 12:44
- Example 25:30
- Example 310:46
- Energy Stored in a Capacitor15:25
- Work is Done Charging a Capacitor15:28
- Solve For That15:55
- Field Energy Density18:09
- Amount of Energy Stored Between the Plates of a Capacitor18:11
- Example18:25
- Dielectrics20:44
- Insulating Materials Place Between Plates of Capacitor to Increase The Devices' Capacitance20:47
- Electric Field is Weakened21:00
- The Greater the Amount of Polarization The Greater the Reduction in Electric Field Strength21:58
- Dielectric Constant (K)22:30
- Formula23:00
- Net Electric Field23:35
- Key Take Away Point23:50
- Example 424:00
- Example 525:50
- Example 626:50
- Example 728:53
- Example 830:57
- Example 932:55
- Example 1034:59
- Example 1137:35
- Example 1239:57

II. Current Electricity

Current & Resistance

17m 59s

- Intro0:00
- Objectives0:08
- Electric Current0:44
- Flow Rate of Electric Charge0:45
- Amperes0:49
- Positive Current Flow1:01
- Current Formula1:19
- Drift Velocity1:35
- Constant Thermal Motion1:39
- Net Electron Flow1:43
- When Electric Field is Applied1:49
- Electron Drift Velocity1:55
- Derivation of Current Flow2:12
- Apply Electric Field E2:20
- Define N as the Volume Density of Charge Carriers2:27
- Current Density4:33
- Current Per Area4:36
- Formula4:44
- Resistance5:14
- Ratio of the Potential Drop Across an Object to the Current Flowing Through the Object5:19
- Ohmic Materials Follow Ohm's Law5:23
- Resistance of a Wire6:05
- Depends on Resistivity6:09
- Resistivity Relates to the Ability of a Material to Resist the Flow of Electrons6:25
- Refining Ohm's Law7:22
- Conversion of Electric Energy to Thermal Energy8:23
- Example 19:54
- Example 210:54
- Example 311:26
- Example 414:41
- Example 515:24

Circuits I: Series Circuits

29m 8s

- Intro0:00
- Objectives0:08
- Ohm's Law Revisited0:39
- Relates Resistance, Potential Difference, and Current Flow0:39
- Formula0:44
- Example 11:09
- Example 21:44
- Example 32:15
- Example 42:56
- Electrical Power3:26
- Transfer of Energy Into Different Types3:28
- Light Bulb3:37
- Television3:41
- Example 53:49
- Example 64:27
- Example 75:12
- Electrical Circuits5:42
- Closed-Loop Path Which Current Can Flow5:43
- Typically Comprised of Electrical Devices5:52
- Conventional Current Flows from High Potential to Low Potential6:04
- Circuit Schematics6:26
- Three-dimensional Electrical Circuits6:37
- Source of Potential Difference Required for Current to Flow7:29
- Complete Conducting Paths7:42
- Current Only Flows in Complete Paths7:43
- Left Image7:46
- Right Image7:56
- Voltmeters8:25
- Measure the Potential Difference Between Two Points in a Circuit8:29
- Can Remove Voltmeter from Circuit Without Breaking the Circuit8:47
- Very High Resistance8:53
- Ammeters9:31
- Measure the Current Flowing Through an Element of a Circuit9:32
- Very Low Resistance9:46
- Put Ammeter in Correctly10:00
- Example 810:24
- Example 911:39
- Example 1012:59
- Example 1113:16
- Series Circuits13:46
- Single Current Path13:49
- Removal of Any Circuit Element Causes an Open Circuit13:54
- Kirchhoff's Laws15:48
- Utilized in Analyzing Circuits15:54
- Kirchhoff's Current Law15:58
- Junction Rule16:02
- Kirchhoff's Voltage Law16:30
- Loop Rule16:49
- Example 1216:58
- Example 1317:32
- Basic Series Circuit Analysis18:36
- Example 1422:06
- Example 1522:29
- Example 1624:02
- Example 1726:47

Circuits II: Parallel Circuits

39m 9s

- Intro0:00
- Objectives0:16
- Parallel Circuits0:38
- Multiple Current Paths0:40
- Removal of a Circuit Element May Allow Other Branches of the Circuit to Continue Operating0:44
- Draw a Simple Parallel Circuit1:02
- Basic Parallel Circuit Analysis3:06
- Example 15:58
- Example 28:14
- Example 39:05
- Example 411:56
- Combination Series-Parallel Circuits14:08
- Circuit Doesn't Have to be Completely Serial or Parallel14:10
- Look for Portions of the Circuit With Parallel Elements14:15
- Lead to Systems of Equations to Solve14:42
- Analysis of a Combination Circuit14:51
- Example 520:23
- Batteries28:49
- Electromotive Force28:50
- Pump for Charge29:04
- Ideal Batteries Have No Resistance29:10
- Real Batteries and Internal Resistance29:20
- Terminal Voltage in Real Batteries29:33
- Ideal Battery29:50
- Real Battery30:25
- Example 631:10
- Example 733:23
- Example 835:49
- Example 938:43

RC Circuits: Steady State

34m 3s

- Intro0:00
- Objectives0:17
- Capacitors in Parallel0:51
- Store Charge on Plates0:52
- Can Be Replaced with an Equivalent Capacitor0:56
- Capacitors in Series1:12
- Must Be the Same1:13
- Can Be Replaced with an Equivalent Capacitor1:15
- RC Circuits1:30
- Comprised of a Source of Potential Difference, a Resistor Network, and Capacitor1:31
- RC Circuits from the Steady-State Perspective1:37
- Key to Understanding RC Circuit Performance1:48
- Charging an RC Circuit2:08
- Discharging an RC Circuit6:18
- The Time Constant8:49
- Time Constant8:58
- By 5 Time Constant9:19
- Example 19:45
- Example 213:27
- Example 316:35
- Example 418:03
- Example 519:39
- Example 626:14

RC Circuits: Transient Analysis

1h 1m 7s

- Intro0:00
- Objectives0:13
- Charging an RC Circuit1:11
- Basic RC Circuit1:15
- Graph of Current Circuit1:29
- Graph of Charge2:17
- Graph of Voltage2:34
- Mathematically Describe the Charts2:56
- Discharging an RC Circuit13:29
- Graph of Current13:47
- Graph of Charge14:08
- Graph of Voltage14:15
- Mathematically Describe the Charts14:30
- The Time Constant20:03
- Time Constant20:04
- By 5 Time Constant20:14
- Example 120:39
- Example 228:53
- Example 327:02
- Example 444:29
- Example 555:24

III. Magnetism

Magnets

8m 38s

- Intro0:00
- Objectives0:08
- Magnetism0:35
- Force Caused by Moving Charges0:36
- Dipoles0:40
- Like Poles Repel, Opposite Poles Attract0:53
- Magnetic Domains0:58
- Random Domains1:04
- Net Magnetic Field1:26
- Example 11:40
- Magnetic Fields2:03
- Magnetic Field Strength2:04
- Magnets are Polarized2:16
- Magnetic Field Lines2:53
- Show the Direction the North Pole of a Magnet Would Tend to Point if Placed on The Field2:54
- Direction3:25
- Magnetic Flux3:41
- The Compass4:05
- Earth is a Giant Magnet4:07
- Earth's Magnetic North Pole4:10
- Compass Lines Up with the Net Magnetic Field4:48
- Magnetic Permeability5:00
- Ratio of the magnetic Field Strength Induced in a Material to the Magnetic Field Strength of the Inducing Field5:01
- Free Space5:13
- Permeability of Matter5:41
- Highly Magnetic Materials5:47
- Magnetic Dipole Moment5:54
- The Force That a Magnet Can Exert on Moving Charges5:59
- Relative Strength of a Magnet6:04
- Example 26:26
- Example 36:52
- Example 47:32
- Example 57:57

Moving Charges In Magnetic Fields

29m 7s

- Intro0:00
- Objectives0:08
- Magnetic Fields0:57
- Vector Quantity0:59
- Tesla1:08
- Gauss1:14
- Forces on Moving Charges1:30
- Magnetic Force is Always Perpendicular to the Charged Objects Velocity1:31
- Magnetic Force Formula2:04
- Magnitude of That2:20
- Image2:29
- Direction of the Magnetic Force3:54
- Right-Hand Rule3:57
- Electron of Negative Charge4:04
- Example 14:51
- Example 26:58
- Path of Charged Particles in B Fields8:07
- Magnetic Force Cannot Perform Work on a Moving Charge8:08
- Magnetic Force Can Change Its Direction8:11
- Total Force on a Moving Charged Particle9:40
- E Field9:50
- B Field9:54
- Lorentz Force9:57
- Velocity Selector10:33
- Charged Particle in Crosses E and B Fields Can Undergo Constant Velocity Motion10:37
- Particle Can Travel Through the Selector Without Any Deflection10:49
- Mass Spectrometer12:21
- Magnetic Fields Accelerate Moving Charges So That They Travel in a Circle12:26
- Used to Determine the Mass of An Unknown Particle12:32
- Example 313:11
- Example 415:01
- Example 516:44
- Example 617:33
- Example 719:12
- Example 819:50
- Example 924:02
- Example 1025:21

Forces on Current-Carrying Wires

17m 52s

- Intro0:00
- Objectives0:08
- Forces on Current-Carrying Wires0:42
- Moving Charges in Magnetic Fields Experience Forces0:45
- Current in a Wire is Just Flow of Charges0:49
- Direction of Force Given by RHR4:04
- Example 14:22
- Electric Motors5:59
- Example 28:14
- Example 38:53
- Example 410:09
- Example 511:04
- Example 612:03

Magnetic Fields Due to Current-Carrying Wires

24m 43s

- Intro0:00
- Objectives0:08
- Force on a Current-Carrying Wire0:38
- Magnetic Fields Cause a Force on Moving Charges0:40
- Current Carrying Wires0:44
- How to Find the Force0:55
- Direction Given by the Right Hand Rule1:04
- Example 11:17
- Example 22:26
- Magnetic Field Due to a Current-Carrying Wire4:20
- Moving Charges Create Magnetic Fields4:24
- Current-Carrying Wires Carry Moving Charges4:27
- Right Hand Rule4:32
- Multiple Wires4:51
- Current-Carrying Wires Can Exert Forces Upon Each Other4:58
- First Right Hand Rule5:15
- Example 36:46
- Force Between Parallel Current Carrying Wires8:01
- Right Hand Rules to Determine Force Between Parallel Current Carrying Wires8:03
- Find Magnetic Field Due to First Wire, Then Find Direction of Force on 2nd Wire8:08
- Example8:20
- Gauss's Law for Magnetism9:26
- Example 410:35
- Example 512:57
- Example 614:19
- Example 716:50
- Example 818:15
- Example 918:43

The Biot-Savart Law

21m 50s

- Intro0:00
- Objectives0:07
- Biot-Savart Law0:24
- Brute Force Method0:49
- Draw It Out0:54
- Diagram1:35
- Example 13:43
- Example 27:02
- Example 314:31

Ampere's Law

26m 31s

- Intro0:00
- Objectives0:07
- Ampere's Law0:27
- Finds the Magnetic Field Due to Current Flowing in a Wire in Situations of Planar and Cylindrical Symmetry0:30
- Formula0:40
- Example1:00
- Example 12:19
- Example 24:08
- Example 36:23
- Example 48:06
- Example 511:43
- Example 613:40
- Example 717:54

Magnetic Flux

7m 24s

- Intro0:00
- Objectives0:07
- Magnetic Flux0:31
- Amount of Magnetic Field Penetrating a Surface0:32
- Webers0:42
- Flux1:07
- Total Magnetic Flux1:27
- Magnetic Flux Through Closed Surfaces1:51
- Gauss's Law for Magnetism2:20
- Total Flux Magnetic Flux Through Any Closed Surface is Zero2:23
- Formula2:45
- Example 13:02
- Example 24:26

Faraday's Law & Lenz's Law

1h 4m 33s

- Intro0:00
- Objectives0:08
- Faraday's Law0:44
- Faraday's Law0:46
- Direction of the Induced Current is Given by Lenz's Law1:09
- Formula1:15
- Lenz's Law1:49
- Lenz's Law2:14
- Lenz's Law2:16
- Example2:30
- Applying Lenz's Law4:09
- If B is Increasing4:13
- If B is Decreasing4:30
- Maxwell's Equations4:55
- Gauss's Law4:59
- Gauss's Law for Magnetism5:16
- Ampere's Law5:26
- Faraday's Law5:39
- Example 16:14
- Example 29:36
- Example 311:12
- Example 419:33
- Example 526:06
- Example 631:55
- Example 742:32
- Example 848:08
- Example 955:50

IV. Inductance, RL Circuits, and LC Circuits

Inductance

6m 41s

- Intro0:00
- Objectives0:08
- Self Inductance0:25
- Ability of a Circuit to Oppose the Magnetic Flux That is Produced by the Circuit Itself0:27
- Changing Magnetic Field Creates an Induced EMF That Fights the Change0:37
- Henrys0:44
- Function of the Circuit's Geometry0:53
- Calculating Self Inductance1:10
- Example 13:40
- Example 25:23

RL Circuits

42m 17s

- Intro0:00
- Objectives0:11
- Inductors in Circuits0:49
- Inductor Opposes Current Flow and Acts Like an Open Circuit When Circuit is First Turned On0:52
- Inductor Keeps Current Going and Acts as a Short1:04
- If the Battery is Removed After a Long Time1:16
- Resister Dissipates Power, Current Will Decay1:36
- Current in RL Circuits2:00
- Define the Diagram2:03
- Mathematically Solve3:07
- Voltage in RL Circuits7:51
- Voltage Formula7:52
- Solve8:17
- Rate of Change of Current in RL Circuits9:42
- Current and Voltage Graphs10:54
- Current Graph10:57
- Voltage Graph11:34
- Example 112:25
- Example 223:44
- Example 334:44

LC Circuits

9m 47s

- Intro0:00
- Objectives0:08
- LC Circuits0:30
- Assume Capacitor is Fully Charged When Circuit is First Turned On0:38
- Interplay of Capacitor and Inductor Creates an Oscillating System0:42
- Charge in LC Circuit0:57
- Current and Potential in LC Circuits7:14
- Graphs of LC Circuits8:27

V. Maxwell's Equations

Maxwell's Equations

3m 38s

- Intro0:00
- Objectives0:07
- Maxwell's Equations0:19
- Gauss's Law0:20
- Gauss's Law for Magnetism0:44
- Faraday's Law1:00
- Ampere's Law1:18
- Revising Ampere's Law1:49
- Allows Us to Calculate the Magnetic Field Due to an Electric Current1:50
- Changing Electric Field Produces a Magnetic Field1:58
- Conduction Current2:33
- Displacement Current2:44
- Maxwell's Equations (Complete)2:58

VI. Sample AP Exams

1998 AP Practice Exam: Multiple Choice Questions

32m 33s

- Intro0:00
- 1998 AP Practice Exam Link0:11
- Multiple Choice 360:36
- Multiple Choice 372:07
- Multiple Choice 382:53
- Multiple Choice 393:32
- Multiple Choice 404:37
- Multiple Choice 414:43
- Multiple Choice 425:22
- Multiple Choice 436:00
- Multiple Choice 448:09
- Multiple Choice 458:27
- Multiple Choice 469:03
- Multiple Choice 479:30
- Multiple Choice 4810:19
- Multiple Choice 4910:47
- Multiple Choice 5012:25
- Multiple Choice 5113:10
- Multiple Choice 5215:06
- Multiple Choice 5316:01
- Multiple Choice 5416:44
- Multiple Choice 5517:10
- Multiple Choice 5619:08
- Multiple Choice 5720:39
- Multiple Choice 5822:24
- Multiple Choice 5922:52
- Multiple Choice 6023:34
- Multiple Choice 6124:09
- Multiple Choice 6224:40
- Multiple Choice 6325:06
- Multiple Choice 6426:07
- Multiple Choice 6527:26
- Multiple Choice 6628:32
- Multiple Choice 6729:14
- Multiple Choice 6829:41
- Multiple Choice 6931:23
- Multiple Choice 7031:49

1998 AP Practice Exam: Free Response Questions

29m 55s

- Intro0:00
- 1998 AP Practice Exam Link0:14
- Free Response 10:22
- Free Response 210:04
- Free Response 316:22

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1 answer

Last reply by: Professor Dan Fullerton

Mon Jun 25, 2018 6:27 AM

Post by Laura Darrow on June 24 at 06:22:28 PM

Hello Mr. Fullerton,

Can you please tell me what's wrong with my calculation regarding the electric potential in Example IV - thank you.

V=(k*q)/r

V=9*10^9*-2/3

V=-6*10^9V

1 answer

Last reply by: Professor Dan Fullerton

Tue Feb 27, 2018 8:37 AM

Post by Kevin Fleming on February 27 at 08:06:27 AM

Professor Fullerton,

Sorry to bother you again. In part a of the 2013 Frq, shouldn't the Q(Enclosed) be just equal to zero. There are no charges inside the gaussian surface that we are using, right?

3 answers

Last reply by: Professor Dan Fullerton

Fri Feb 23, 2018 6:50 AM

Post by Kevin Fleming on February 22 at 07:33:06 AM

Proffesor Fullerton,

Since W = -U (Or potential energy), and W = QV, wouldn't electrical potential energy be U = -QV, not just QV? Thanks.

1 answer

Last reply by: Professor Dan Fullerton

Fri Apr 8, 2016 6:12 AM

Post by Ayberk Aydin on April 7, 2016

For example 8, isn't the electric field directed opposite the displacement? So there should be a negative multiplier? And isn't the charge of the electron at the end negative also? Or did you just realize those two negative would cancel out at the end?

1 answer

Last reply by: Professor Dan Fullerton

Mon Jan 18, 2016 7:20 AM

Post by Shehryar Khursheed on January 17, 2016

Hello Mr. Fullerton, I have a question about the 2003 FRQ, part e.

You used an integral to find the charge enclosed within the gaussian region. When I attempted this problem on my own, I did not use an integral. This is what I did:

1) q=(rho)V

2) Because we are interested in a specific "r", we can just plug in the values for an arbitrary "r" within the spherical cloud.

3) A specific region enclosed will have a volume of (4/3)(pi)r^3, therefore...

4)Qenc= (rho not)(1-(r/R))*((4/3)(pi)r^3)

5)I plugged this into Gauss's Law and ended up with a similar answer, except I did not have a 3/4 in the fraction of r/R

I was wondering, why didn't this approach work. Even if the charge density isn't uniform, I can still plug in the function as long as I have the same function of the volume, can't I? I hope you understand what I'm trying to ask because I'm not sure if I can explain my problem best in writing. Thanks!

1 answer

Last reply by: Professor Dan Fullerton

Sun Apr 5, 2015 6:42 AM

Post by Luvivia Chang on April 4, 2015

hello Professor Dan Fullerton,

why is Electric force F=-du/dl insiead of du/dl?

why is the "-" there ?

1 answer

Last reply by: Professor Dan Fullerton

Sun Mar 29, 2015 9:39 AM

Post by holly song on March 28, 2015

why I keep getting network error message and couldn't watch your lessons? Thanks!