Question

Let $\overrightarrow{E}$ and $\overrightarrow{B}$ denote electric and magnetic fields in a frame S and $\overrightarrow{E\text{'}}$ and $\overrightarrow{B\text{'}}$ in another frame S' moving with respect to S at a velocity $\overrightarrow{v}$. Two of the following equations are wrong. Identify them.
(a) $B_y\text{'}=B_y+\frac{v{E}_z}{c^2}$

(b) $E_y\text{'}=E_y-\frac{v{B}_z}{c^2}$

(c) B_y' = B_y + vE_z

(d) E_y' = E_y + vB_z

Answer 1

(b) E_y^' = E_y - $\frac{v{B}_z}{c^2}$
(c) $B_{\mathrm{y}}^{\text{'}}=B_{\mathrm{y}}+v{E}_{\mathrm{z}}$

Electric force due to a charged particle is q E and magnetic force is q V B.

We can sort out the two wrong equations using dimensional analysis. Now, equating the above two forces. we get:

E = V B

Hence, analysing the answers using dimensional analysis, we see that the second term on the RHS of the equations (b) and (c) are not dimensionally correct. Thus, the options (b) and (c) are wrong.