Week 8

Question 1

Derive the electrostatic energy in the electric field

Answer 1

WE DO NOT NEED TO DERIVE THIS, just use:

The work one needs to do to overcome the Coulomb force and construct a system of charges in electrostatics can be written in terms of the potentials:

Question 2

Derive the Energy stored in a current in magnetostatics

Answer 2

WE DO NOT NEED TO DERIVE THIS, JUST USE:

Question 3

Generalise the energy stored in a current to a surface current or volume current

Answer 3

WE DO NOT NEED TO DERIVE THIS, JUST USE:

Question 4

Derive the energy over all space in a static magnetic field

Answer 4

WE DO NOT NEED TO DERIVE THIS, JUST USE:

Question 5

Derive Poyntings theorem

Answer 5

WE DO NEED TO DERIVE THIS:

Using Lorentz’s force law F = Q(E + vxB) is work done on a charge Q moving with velocity v therefore:

Question 6

Poynting Vector

Answer 6

Which is the energy flux density

Question 7

D’ambertian

Answer 7

μ₀ε₀ = 1/(c**2)

It is the natural extension of the laplacion to a 4D space time operator

Question 8

Use Gauss’s law and Ampere’s law (with Maxwell term) to develop laplacians for E and B

Answer 8

Check this lol

Question 9

Develop laplacians into decoupled Maxwell equations using Lorenz gauge

Answer 9

The final 2 lines then can use the D’alembertian

Question 10

D’alembertian was on laplacians

Answer 10

Question 11

Retarded time

Answer 11

Time for light to travel across s

Question 12

Derive retarded and advanced potentials

Answer 12

THIS IS NOT ON EXAM