Question regarding Magnetic field

[utkarshakash]

Homework Statement

Let $\vec{E}$ and $\vec{B}$ denote electric and magnetic fields in a frame S and $\vec{E'}$ and $\vec{B'}$ in another frame S' moving with respect to S at a velocity $\vec{v}$. Two of the following equations are wrong. Identify them.

a)$B_y ' = B_y + \dfrac{vE_z}{c^2}$
b)$E_y ' = E_y - \dfrac{vB_z}{c^2}$
c)$b_y ' = B_y + vE_z$
d)$E_y ' = E_y + vB_z$

Homework Equations

The Attempt at a Solution

First of all I can't understand what is 'c' here. Is it speed of light?Also, how can the magnitude of field change with frame? The magnitude of force can vary but I don't think field should vary. This question seems too complicated to me.

 

[WannabeNewton]

$c$ is the speed of light yes. The magnetic and electric fields transform non-trivially under Lorentz boosts; one can prove this using special relativity. You can probably look it up online if you don't have a textbook that discusses it.

 

[jtbell]

Dimensional analysis might be useful here.

 

[utkarshakash]

Dimensional analysis might be useful here.

Hmm... So its just basically a problem of dimensional analysis. No magnetics involved.