# Physics 511A, 2014: Chapter 3, Volume 2. Charges in electromagnetic field

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## Homework Questions

1. Derive the formula for ${\displaystyle \nabla \left({\vec {a}}\cdot {\vec {b}}\right)}$.
2. Problem after Section 17.
3. Prove that ${\displaystyle {\frac {d\varepsilon }{dt}}={\vec {v}}\cdot {\frac {d{\vec {p}}}{dt}}}$.
4. Verify by direct calculation that the gauge transformation (18.3) doesn't change the equation of motion of a particle in an electromagnetic field.
5. Problem after Section 21.
6. Problem 1 after Section 22.
7. Problem after Section 25.
8. Show the equivalence of the 4-d and the 3-d version of the equations of motion of a particle in a field.
9. Problems 1 and 2 after Section 6.
10. Derive ${\displaystyle v/c\to 0}$ limit of the equations for Lorentz transformation of ${\displaystyle H,E}$.