Please review Section 10.1 and Ch. 12.
- (p. 420, Problem 10.3) - GIVEN V & . . .
Find the , , & corresponding to
- 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?
- (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?
- 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
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.
Jess H. Brewer