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. $\mu_{0}\varepsilon_{0}\left( \frac{B}{E} \right)^{2}$
• D. $\frac{E}{\varepsilon_{0}}\frac{\mu_{0}}{B}$

Answer 1

Answer: (A)

$\sqrt{\mu_{0}\varepsilon_{0}}\frac{E}{B}$

Answer 2

: 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.