Physics 511A, 2014: Chapter 4, Volume 2. Electromagnetic field equations

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Back to Physics 511A, 2014: 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 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \delta(x)} function transforms under reparameterization $x\to y=y(x)$.
3. Show that the four-current is a four-vector, explicitly component-by-component.
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 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle v/c} , what is the energy-momentum tensor of ordinary, nonrelativistic matter.
10. Calculate Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle T_i^i} for electromagnetic field with no charges.