PHYS5140 (2023-24 Term1)
Homework 6
Due: 25/11/2023 Sat (before 11:59 pm)
Submit your answers via Blackboard
Total marks= 70 (3 problems)
1. (24 marks) Given two equal point charges q, separated by a distance 2. Construct the
plane equidistant from the two charges. Determine the force of one charge on the other by
integrating Maxwell’s stress tensor over this plane.
2. (20 marks) Given the following set of potentials:
{
(⃗, ) = ()
(⃗, ) = ()̂
Where and are constants.
(a) If the potentials satisfy Lorentz gauge, find a possible expression for the function ()
(b) Using your answer in (a), find the electric field and magnetic field.
3. (26 marks) An infinitely long straight wire with a current flowing in the z direction. The
current is given by
() = {
0 ≤ 0
2 > 0
Find the retarded scalar and vector potentials at any point at some finite distance away from
the wire.