Question

If $E$ and $B$ denote electric and magnetic fields respectively, which of the following is dimensionless ?

• A. $\sqrt{\mu _{0}\varepsilon _{0}} \frac{E}{B} $
• B. $\mu _{0}\varepsilon _{0} \frac{E}{B} $
• C. $\mu _{0}\varepsilon _{0}\left( \frac{E}{B} \right)^{2}$
• D. $ \frac{E}{\varepsilon _{0}} \frac{ \mu _{0} }{B}$

Answer 1

Answer: (A)

Speed of light,
$c = \frac{1}{\sqrt{\mu_{0}\varepsilon_{0}}}$;
Also, $\frac{E}{B} = c$
Therefore, $\sqrt{\mu _{0}\varepsilon _{0}} \frac{E}{B}$ is dimensionless.