THE UNIVERSITY OF BRITISH COLUMBIA

*Physics 401 *
Assignment #
**4:**

** POTENTIALS, GAUGES and RELATIVITY **

Wed. 25 Jan. 2006 - finish by Wed. 1 Feb.

Please review Section 10.1 and Ch. 12.
Wed. 25 Jan. 2006 - finish by Wed. 1 Feb.

- (p. 420, Problem
**10.3**) -**GIVEN**Find the , , & corresponding to*V*& . . .

**POINT CHARGE:**- Find the and fields corresponding to
a stationary point charge
*q*situated at the origin. - State the charge and current distributions of this situation.
- What are the electric and magnetic potentials?
- Is there any relation between this situation
and that described in Problem
**10.3**?

- Find the and fields corresponding to
a stationary point charge
- (p. 420, Problem
**10.5**) -**GAUGE TRANSFORMATION:**Use the gauge function

to transform the potentials in Problem**10.3**, and comment on the result. **WHICH GAUGE?**- In Problem
**10.3**above, are the potentials in the Coulomb gauge, the Lorentz gauge, both, or neither? - In Problem 2 above, are the potentials in the Coulomb gauge, the Lorentz gauge, both, or neither?

- In Problem
**NATURAL UNITS:**Since*c*is now a*defined*quantity that keeps appearing in confusing places in our notation for 4-vectors*etc.*, and since*nanoseconds*(ns) are perfectly handy units for*distance*, it seems silly to not just measure time and distance in the same units (seconds) and set*c*=1. While we're at it, why not set the ubiquitous constant in quantum mechanics to unity as well () so that all angular momenta are unitless and (because ) energies are measured in s^{-1}?- In what units would we then measure velocities, momenta, masses, forces and accelerations?
- Suppose we set the Coulomb force constant
as well. In what units would we then measure charge, electric field,
magnetic field, and potentials
*V*and ? - Write out Maxwell's equations in this system of units.
(
*Hint:*We must have .)^{1}

**4-POTENTIAL:**In Eq. (12.131) on p. 541, Griffiths states that, "As you might guess,*V*and together constitute a 4-vector: ." This is a very strong statement with profound consequences. You can't just take any 3-vector and combine it with a convenient scalar in the same units to make a true 4-vector!*Explain why*we should believe this about , and list any essential*conditions*that must be met for it to be true.

2006-01-24