Special Relativity - Electromagnetic Field

Which of the following statements most accurately describes how an electromagnetic field behaves under a Lorentz transformation?

1. The electric field transforms completely into a magnetic field.
2. If initially there is only an electric field, after the transformation there maybe both an electric and magnetic field.
3. The electric field is unaltered.
4. The magnetic field is unaltered.
5. It cannot be determined unless a gauge transformation is also specified.

(GR8677 #22)

Solution:

see analysis: Electromagnetism and Relativity

Answer: A

Special Relativity - Lorentz transformation

Which of the following is a Lorentz transformation? (Assume a system of units such that the velocity of light is 1.)

A.

B.

C.

D.

E. None of the above

(GR9277 #94)

Solution:

Galilean	Lorentz
x' = x − vt	x' = (x − vt)γ
y' = y	y' = y
z' = z	z' = z
t' = t	t' = (t − vx/c²)γ

A and B are FALSE since t' = t is Galilean.

Check answer C:
x' =  (x − vt)γ = 1.25x − .75t
γ = 1.25 and vγ = .75
v = .75/1.25

t' = (t − vx/c²)γ = 1.25t − .75x
γ = 1.25 and (v/c²)γ = .75
v = .75c²/1.25 = .75/1.25, since  c = 1


v is consistent → C is TRUE

Answer: C