Physics 511A, 2012: Chapter 4, Volume 2. Electromagnetic field equations

Back to the main Teaching page.

Back to Physics 511A, 2012: Graduate Electrodynamics.

Homework Questions

1. Verify explicitly the equivalence between Eqs. 26.5 and the first pair of Maxwell's equations, 26.1 and 26.2.
2. Verify how the δ(x) function transforms under reparameterization $x\to y=y(x)$.
3. Show that the four-current is a four-vector (for this you need to recall how densities and distributions transform, Chapter 1).
4. Derive the expression for a magnetic field of a constant current line using Eq. 30.8
5. Verify the charge continuity equation for a single moving charge.
6. Explain how gauge invariance is a direct consequence of charge conservation under Lorentz transformations.
7. Problem after Sec 33.
8. Derive Eq 33.5.
9. To the leading order in v / c, what is the energy-momentum tensor of ordinary, nonrelativistic matter.
10. Calculate $T_i^i$ for electromagnetic field with no charges.