Electric Potential & UE Lesson 04





  • Test Charge: A mathematical construct-- a charge that does not exert any influence on surrounding particles but IS influenced by other electric fields.
  • conductor - materials where electrons can roam
  • insulator - materials that keep their electrons close to home
  • coulomb - a unit of electrical charge (see below)


  • e-mass = 9.1 x 10-31 kg
  • charge of an electron = 1.60 x 10-19 coulombs (C)
  • ke = 8.987 x 109 Nm2/C2
  • ke = 1/4πεo


      • Electric Potential (V) and Electric Potential Energy (UE)
        • U = -qE ds
        • Vb - Va = ∆V = U/q = -E ds
        • W = qV = -UE
        • V = keqi/ri (between some point in space and each charged particle present in that region of space)
        • V = kedq/r
        • UE = keq1q2/ri (between each particle in space and every other particle in that region of space)
        • Ex = -dV/dx
      • Electrical Force:
        • Fe = (keq1q2)/r2
        • Fe=qE
      • Electrical Field:
        • E = Fe / qo where qo  = a positive test charge
        • E= (keq)/r2
      • Gauss's Law:

        Φ = E A dA

        Φ = qin/εo : the electric flux through an ENTIRE gaussian surface is equal to the algebraic sum of the charges INSIDE the surface divided by the permitivity of free space

WORK O' THE DAY (revised):

Please review each other's homework from yesterday... Make SURE you can do the integration. Pay particular attention to using λ as a way to 'build a bridge' between different variables... for example if you are integrating dq/r, you MUST have q in terms of r or r in terms of q. λ lets us do that.

I have thes following questions printed out. DO NOT treat this as a task to be completed, that's useless... use it as a prompt to help you identify what you know, what you kinda know and what you don't know.

1) What is the significance of use s or ds when calculating electric potential? That is to say why don't we use dr or dx instead?

2a) Compare electric potential (voltage) and potential energy.

2b) Contrast electric potential (voltage) and potential energy.

3) When we integrate Eds, why is the upper limit "b" and the lower limit "a"? Wouldn't it be a whole lot easier to integrate from "a" to "b"?

4) How do we calculate electric force in terms of the electric field?

5) What is Coulomb's Law?

6) What is the numeric value of the electrical constant?

6b) What is the more symbol-based value of the electrical constant?

7) When your *most gracious and humble* physics instructor suggests that we treat


as a check list, what the heck is he talking about?

7) We can ALWAYS find _____ in an enclose area using Gauss's Law, however it can be AWFULLY difficult to the find the __________ unless we can determine that the __________ is constant and that the angle the Efield lines make to the surface area vector (known as _____) is also __________.

8) Oh and by the way (insulators/conductors) do NOT make Gaussian Surfaces because ___________________.

9) When you (not me, I ain't got no hair) rub a balloon against your hair, the balloon MUST be made of a/an insulator/conductor because if it was made of a/an (insulator/conductor) the electrons would simply redistribute themselves and there would be no area of unequal charge distribution.

10) What is the significance of the surface integral: ?

11) What is the definition of electric potential? (trick question: how is it different from potential difference?)

12) What is the relationship between voltage and work?

13) What are the various mathematical equations that relate Efield to voltage? (show me at least 3)

14) What is the relationship between multiple point charges and voltage?

15) What integral gives us that relationship?

16) What is the relationship between voltage and potential energy?


We've lost 5 days with all the snow days and late starts. So hey, sucks to be us... We'll test on the Tuesday after the break.

If you wait until Sunday to try and get caught up, you won't.

If your GPA is of particular importance, you definitely DO NOT want to start out second semester with a poor grade. The work will only get harder as we go.

To wit:

I'll be treating Midwinter Break as a working vacation. I have some ideas for study guides and such so PLEASE check the website.

In the meantime, please go HERE and complete that form

I'll be adding additional questions, answers and study guides ON THE CALENDAR during the break. I'll also take requests for help study guides etc..... please, please, please, don't make it that I work harder on this than you do.

I won't answer ANY questions after noon on Sunday before we return