2.4 LT of the 4-Tensor

Question 1

What properties does a rank 0 tensor have?

Answer 1

It is an invariant scalar

- Same in every frame

Question 2

How is the electric field in the direction of the Lorentz boost changed?

Answer 2

It is unchanged

Question 3

How is the magnetic field in the direction of the Lorentz boost changed?

Answer 3

It is unchanged

Question 4

How are the perpendicular components of the electric field changed under a Lorentz boost?

Answer 4

E’ = γ(E + v x B)

Question 5

How are the perpendicular components of the magnetic field changed under a Lorentz boost?

Answer 5

B’ = γ(B - (v x E)/c^2)

Question 6

How are E and B related in terms of frame invariance?

Answer 6

E . B = E’ . B’ and (E/c)^2 -B^2 = etc

Question 7

What does the determinant of the contravariant Faraday tensor give you?

Answer 7

det ( F^(alpha beta)) = (E.B)^2

Question 8

What is the invariant scalar of the Faraday tensor equal to? (Multiply contravariant and covariant)

Answer 8

E^2 / c^2 - B^2