Question

Consider the following cylindrically symmetric potentials:
?(?,?)= 0 ?(?,?) = −?0t/2piE0? a Find the corresponding electric and magnetic fields ??,? and ??,?.
b. Find the scalar gauge function ?(?,?) that transforms these potentials to a more familiar form where only the scalar potential is non-zero. Note that this ? is not the same as the ?! that shows up in the potentials.

Answer 1

Electric field in terms of potentials is

The given potentials are

Hence,

Magnetic field in terms of potential is

The expression of curl in cylindrical coordinates is

From equation (3) we can see that and is only a function of , therefore

Under a gauge transformation the potentials transform as

We want

Therefore