Question

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

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

Answer 1

Answer: (B), (C)

The correct options are
B $E_y^{\prime }=E_y-\frac{v{B}_z}{c^2}$
C $B_y^{\prime }=B_y+v{E}_z$

Electric force due to a charged particle is $q$$E$ and magnetic force is $qvB$.

So we can find the wrong equation by using dimensional analysis

Now, equating the above two forces and get

$E=VB$

Hence, after analyzing the answers by using dimensional analysis we found that the second term on the right hand side of the equations $\left(b\right)$ and $\left(c\right)$ are not dimension-ally correct.

So the Option $\left(b\right)$ and $\left(C\right)$ are wrong.