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

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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 $\delta (x)$ 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.