• Chapter 22 - Problem 14, Problem 32, Problem 48
• Chapter 23 - Problem 14, Problem 28, Problem 57
• Chapter 24 - Problem 11, Problem 34, Problem 41

Coulomb's Law - example of a Central Force

F12 =  1 4pe0  Q1 Q2 r2   ^ r

Force is attractive if charges have opposite sign.

Electric Dipole

• Two charges +Q, -Q small distance a apart
• Dipole moment p = aQ directed from negative to positive charge
• If at large distance r >> a then
  

  V = p· ^ r   4pe0 r2

• Potential drops as 1/r² (rather than 1/r for point charge)
• Electric field drops as 1/r³ (rather than 1/r²)

• Newton's second law: acceleration = QE/m
• Constant acceleration in direction of E
• No acceleration perpendicular to E
• Sign on charge determines direction of acceleration

Gauss's Law - more general than Coulomb's Law
Only include net charge - that inside Gaussian Surface

Fnet = ó (ç) õ S  En dA =  Qnet e0

Evaluate over a closed surface - the Gaussian surface

Select Gaussian surface and appropriate charge density
(l, s, r). Then sum or integrate.

• No E inside conductor - Potential uniform inside
• Field at surface normal to surface
• Thus, no tangential field - boundary condition
• E = s/e₀
• Surface of conductor is an equipotential

Electric Potential Energy - zero at infinity

U(r) = - ó õ r ¥  F ·dl

Electric force is a conservative force - work done is independent of path (zero for a closed path; Chapter 9)

For a system of charged particles or a distribution

V =  1 4pe0 å i   Qi ri

V =  1 4pe0 ó õ  dQ r

Q1. Taken out of a drier, two socks stick together and two don't. Which pair is the better conductor?

Q2. Released from rest, a positively charged particle will move along an electric field line.
(a) Will the particle follow a straight field line?
(b) Will the particle follow a curved field line?
(c) If not, will its path be more or less curved?

Q3. A closed surface encloses no excess charge.
(a) Is the electric field at each point on the surface zero?
(b) Is the electric flux for the surface zero?

Q4. Suppose two particles with different charge are enclosed by a surface. If they exchange positions does the
(a) flux for the surface change?
(b) field at points on the surface change?

Q5. A positively charged particle is moved in the direction of an electric field. What happens to its electric P.E. ?

Q6. Can equipotential surfaces intersect?

Q7. How would you store a delicate instrument to protect it from stray electric fields?

Q8. Round conducting spheres are often used to protect high-voltage equipment. Why?

Q9. Estimate the smallest radius of curvature that can be used for a conductor at 100,000 V if the breakdown electric field strength for air is 3×10⁶ V m^-1.

Q10. Someone has proposed to build the International Space Station by firing material from the Lunar surface into Earth Orbit using an ``electrostatic gun''. Would this be practical in terms of the electric potential required?

[Moon mass = 7.2 ×10²² kg; Moon Radius 1.74×10⁶ m]