Question

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

• A. $E_y^{\prime }=E_y-\frac{v{B}_z}{c^2}$
• B. $B_y^{\prime }=B_y+\frac{v{E}_z}{c^2}$
• C. $B_y^{\prime }=B_y+v{E}_z$
• D. $E_y^{\prime }=E_y-v{B}_z$

Answer 1

Answer: (A), (C)

From Lorentz transformation,
$E_y^{{}^{\prime }}=\gamma (E_y-v{B}_z)$
$B_y^{{}^{\prime }}=\gamma (B_y+\frac{v}{c^2}{E}_z)$
where $\gamma =\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}$ where the symbols have their usual meaning.
when $\frac{v}{c}<<1$ $\gamma =1$, then the the transformation equations will hold.