# Physics 511A, 2014: Chapter 5, Volume 2. Constant electromagnetic fields

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## Homework Questions

1. Show that ${\displaystyle \Delta {\frac {1}{R}}=-4\pi \delta ({\vec {R}})}$.
2. Problem after Sec 38.
3. Problem 1 after Sec 39.
4. Verify that 39.3 solves the Hamilton-Jacobi equation.
5. Derive the motion of a relativistic charge in a Coulomb field.
6. Derive Eq. 40.8, 40.11.
7. Verify Eq. 41.9.
8. Sketch the field of a dipole and a quadrupole in the most convenient reference frame.
9. Problem after Sec 41. Compare the monopole, the dipole, and the quadrupole field of the ellipsoid at points ${\displaystyle (2a,0,0)}$ and ${\displaystyle (20a,0,0)}$.
10. Derive equations 42.4, 42.6, 42.7, 42.8.
11. Derive equation 44.4 from 44.3.
12. Problem after section 44.