# Field transformation laws - Relativity

1. Sep 13, 2016

### erisedk

1. The problem statement, all variables and given/known data
The electric and magnetic fields of a 1 Coulomb charge Q are measured by a pair of field measuring instruments. From the perspective of observers in frame O, the charge is at rest at the origin and one of the field-measuring devices is also at rest, with position (x,y,z) = (0,1,0). Observers in O see the second field-measuring device moving at high speed, with velocity v = βc (x direction) (it travels along the line y = 1)

(a) At time t = 0 this device passes very close to the stationary device at (x,y,z) = (0,1,0). The readings on the dials of the moving device were photographed by observers in O as it was illuminated by the lights from the stationary device's panel lights.

1. Calculate the components of the electric and magnetic field vectors measured by the stationary device at the time the photograph was taken.

2. Calculate the components of the electric and magnetic field vectors measured by the moving device.

3. According to observers in the rest frame of the moving device, how far away is the charge Q?

2. Relevant equations

3. The attempt at a solution
1. Electric field vector at stationary device = kQ/r2 (j) = (9 × 109 × 1)/12 = 9 × 109 V/m

Magnetic field vector at stationary device = 0 because there is no relative motion between the point charge and the stationary device.

2. I don't understand how to do this at all. We're supposed to used this large matrix (EM strength tensor) I think, but I don't really understand how to do that.

If I were to do it without relativity, I'd just treat Q as a line of charge (or a current carrying wire) and solve, but that's definitely wrong.

3. Wouldn't it keep changing as a function of time?
d = $\sqrt{1^2 + v^2t^2}$ where v = βc