OBJECTIVES:  

WORDS/FORMULAE FOR TODAY

Terms:

• 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)

Constants:

• e^-_mass = 9.1 x 10^-31 kg
• charge of an electron = 1.60 x 10^-19 coulombs (C)
• k_e = 8.987 x 10⁹ Nm²/C²
• k_e = 1/4πε_o

Formulae:

• Electric Potential (V) and Electric Potential Energy (U_E)
  • ∆U = -q∫E ∙ ds
  • V_b - V_a = ∆V = ∆U/q = -∫E ∙ ds
  • W = q∆V = -U_E
  • V = k_e∑q_i/r_i (between some point in space and each charged particle present in that region of space)
  • V = ∫k_edq/r
  • U_E = k_e∑q₁q₂/r_i (between each particle in space and every other particle in that region of space)
  • E_x = -dV/dx
• Electrical Force:
  • F_e = (k_eq₁q₂)/r²
  • F_e=qE
• Electrical Field:
  • E = F_e / q_o where q_o  = a positive test charge
  • E= (k_eq)/r²
• Gauss's Law:

  Φ = ∮E ∙A dA

  Φ = q_in/ε_o : 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):

Ok, so it looks like I overwrote volts 02 right over the top of volts 03....blech, I was cold and cranky... sorry everyone.

To wit... we've got a VERY short day today, and it would be a very good idea for me to see where everyone's at with all of this.... so:

Let's do a quick temperature check.

Please bust out a loose sheet of paper and (working alone if you would please) address the following:

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

∮EcosθdA

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?

UNLESS I'm WELL off the mark, we'll have lots of empty spaces on this one... that's ok, it was a rough week.