Question

Choose the correct answer from the alternatives given.
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. $\frac{E}{{\epsilon }_0}\times \frac{{\mu }_0}{B}$

Answer 1

The correct option is A $\sqrt{{\mu }_0{\epsilon }_0}\frac{E}{B}$

For an electromagnetic wave, we know that,

$\frac{E}{B}=c$ (velocity of light if we consider free space)

and $\frac{1}{\sqrt{{\mu }_0{\epsilon }_0}}=c$

$\therefore \sqrt{{\mu }_0{\epsilon }_0}\times \frac{E}{B}$ is considered to be dimensionless.