Question

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

• A. $\sqrt{\mu _{0} \, \epsilon _{0}}\frac{E}{B}$
• B. $\mu _{0}\epsilon _{0}\frac{E}{B}$
• C. $\mu_0 \varepsilon_0\left(\frac{B}{E}\right)^2$
• D. $\frac{\mu _{0} E}{B \epsilon _{0}}$

Answer 1

Answer: (A)

$\frac{E}{B}=c$ (Velocity of light if we consider free space) and $\frac{1}{\sqrt{\mu _{0} \, \epsilon _{0}}}=c$
So $\sqrt{\mu _{0} \, \epsilon _{0}}\frac{E}{B}$ is dimensionless.