Question

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

• A. $\sqrt{{μ}_0{Ï\mu }_0}\frac{E}{B}$
• B. ${μ}_0{Ï\mu }_0\frac{E}{B}$
• C. ${μ}_0{Î\mu }_0{\left(\frac{B}{E}\right)}^2$
• D. $\frac{{μ}_{0}E}{B{Ï\mu }_0}$

Answer 1

Answer: (A)

$\frac{E}{B}=c$ (Velocity of light if we consider free space) and $\frac{1}{\sqrt{{μ}_0{Ï\mu }_0}}=c$
So $\sqrt{{μ}_0{Ï\mu }_0}\frac{E}{B}$ is dimensionless.