1. Finish EM Ch. 5: Magnetostatics Methods of Math
Finish EM Ch.5: Magnetostatics Methods of Math. Physics, Friday 1 April 2011, E.J. Zita
Review & practice
Lorentz Force
Ampere’s Law
Maxwell’s equations
Magnetic vector potential A || Electrostatic potential V
Multipole expansion
Boundary Conditions

2. Lorentz Force
Problem 5.39 p.247: A current I flows to the right through a rectangular bar of conducting material, in the presence of a uniform magnetic field B pointing out of the page (Fig.5.56).
If the moving charges are positive, in which direction are they deflected by B? Describe the resultant E field in the bar.
Find the resultant potential difference between the top and bottom of the bar (of thickness t and width w) and v, the speed of the charges. Hall Effect!

4. Ampere’s Law
p.231 #13-16
You choose…

5. Ampere’s Law
p.231 #14

6. Ampere’s Law
p.231 #15

7. Ampere’s Law
p.231 #16

8. Four laws of electromagnetism

9. Electrodynamics Changing E(t) make B(x) Changing B(t) make E(x)
Wave equations for E and B
Electromagnetic waves
Motors and generators
Dynamic Sun

10. Full Maxwell’s equations

11. Maxwell’s Eqns with magnetic monopole
Lorentz Force:
Continuity equation:

13. Vector Fields: Potentials.1
For some vector field F = -  V, find F :
(hint: look at identities inside front cover)
F = 0 → F = -V
Curl-free fields can be written as the gradient of a scalar potential (physically, these are conservative fields, e.g. gravity or electrostatic).

14. Theorem 1 – examples
The second part of each question illustrates Theorem 2, which follows…

15. Vector Fields: Potentials.2
For some vector field F = A , find F :
F = 0 → F = A
Divergence-free fields can be written as the curl of a vector potential (physically, these have closed field lines, e.g. magnetic).

16. Practice with vector field theorems

17. Magnetic vector potential

18. Magnetic vector potential

19. Electrostatic scalar potential V

22. Find the vector potential A…
5.27 p.239: Find A above and below a plane surface current flowing over the x-y plane (Ex.5.8 p.226)
B = ____ A || K 

23. Electric dipole expansion of an arbitrary charge distribution r(r). (p
Pn(cosq) are the Legendre Polynomials

24. Magnetic multipole expansion
Vector potential A of a current loop is (5.83) p.244

25. Magnetic field of a dipole
B=A, where

26. Find the magnetic dipole moment of a spinning phonograph record of radius R, carrying uniform surface charge s, spinning at constant angular velocity w. (5.35 – see 6.a)
dI = K dr, m = I area =
HW: 5.58 – see 6.b

27. Boundary conditions See Figs.5.49, 5.50, p.241:

28. 5.31: Check BC for solenoid or spinning shell
Check Eqn for Ex.5.9 (p.277): solenoid.
Check Eqn & 5.76 for Ex (p.236): charged shell