1.1-1.4 Maxwell's Equations and EM Fields Flashcards
What are the source terms in Maxwell’s Equations?
Charges and currents
Which quantities do the source terms lead us on to?
Displacement current, D = epsilon_0 E
Magnetic flux density B = mu_0 H
If magnetic monopoles existed, how would Maxwell’s equations change?
The diveregence of the Magnetic field would no longer equal 0
∇. B would be proportional to the density of the monopoles
When would the divergence of the electric field be equal to 0?
When we are in a charge free region of space
What is the Poynting Vector?
A vector that represents the directional energy flux or power flow of an EM field
What is the equation for the Poynting vector?
S = E x H
What is the equation for impedence?
Z = |E| / |H|
What is the impedence of free space?
Z_0 = 377 Ohms
What are the two potentials that we deal with in EM?
Vector potential A
Scalar potential ϕ
Give some examples of a Vector potential that will give a magnetic field of B_0 z
A = B_0 (0, x, 0) A = B_0 (-y, 0, 0) A = B_0/2 (-y, x, 0)
How are B and A related as an equation and graphically?
B = curl A
B points up in the Z direction, A is in circulation (like RH Rule)
What is the Coulomb gauge and when is it useful?
When the divergence of A = 0
∇. A = 0
Useful for plane waves
What is the Lorentz gauge and when is it useful?
∇. A + 1/c^2 (dϕ/dt) = 0
Useful for relativity
What is the d’Alembertian operator?
The Laplace operator of Minkowski space
◻ = 1/c^2 (d^2/dt^2) - ∇^2
What is the result when you act on the vector potential, A with the d’Alembertian operator?
◻A = μ0 j
