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. ${\mu }_0{\epsilon }_0{\left(\frac{E}{B}\right)}^2$
• D. $\frac{E}{{\epsilon }_0}\frac{{\mu }_0}{B}$

Answer 1

Answer: (A)

Speed of light,
$c=\frac{1}{\sqrt{{\mu }_0{\epsilon }_0}}$;
Also, $\frac{E}{B}=c$
Therefore, $\sqrt{{\mu }_0{\epsilon }_0}\frac{E}{B}$ is dimensionless.