Week 1 Electromagnetism and Wave Equation

Question 1

what are the four Maxwell equations

Answer 1

∇B = 0
∇xE = -dB/dt
∇E = ρ/ε0
∇xB - μ0ε0 = μ0j

Question 2

what are the two EM wave equations

Answer 2

∇^2B = 1/c^2 d^2B/dt^2
∇^2E = 1/c^2 d^

Question 3

what is the plane wave eqn

Answer 3

E = Aexp[i(kr-ωt)]

Question 4

what is the mutual orthogonality eqn

Answer 4

k x E = ωB

Question 5

what is the Poynting Vector eqn

Answer 5

N = 1/μ E x B

Question 6

how is the 1D wave equation solved

Answer 6

by factorising

Question 7

what is the Helmholtz eqn

Answer 7

∇^2Er = -k^2Er

Question 8

define the Huygens-Fresnel principle

Answer 8

If you have a wavefront and want to know how it looks at a later time you draw points and assume they have secondary wavelets. Wavelets destructively interfere in all directions bar one

Question 9

what is the Obliquity factor eqn

Answer 9

1/2(1 + cosθ)

Question 10

what is Fermatt’s principle

Answer 10

light ray going from a to B traverses a path that is stationary with respect to variations in optical path (path of least time)