Question

If E and B denote electronic and magnetic field 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. ${\mu }_0{\epsilon }_0{\left(\frac{B}{E}\right)}^2$
• D. $\frac{E}{{\epsilon }_0}\frac{{\mu }_0}{B}$

Answer 1

Answer: (A)

$\sqrt{{\mu }_0{\epsilon }_0}\frac{E}{B}$

We know that Velocity of light $C_0=\frac{1}{\sqrt{{\mu }_0{ϵ}_0}}$

And also velocity of electromagnetic wave $V=\frac{E}{B}$

$\left[C_0\right]=\left[\frac{1}{\sqrt{{\mu }_0{ϵ}_0}}\right]=\left[L{T}^{-1}\right]$

$\left[V\right]=\left[\frac{E}{B}\right]=\left[L{T}^{-1}\right]$

$\left[\sqrt{{\mu }_0{\epsilon }_0}\frac{E}{B}\right]=\left[L{T}^{-1}{]}^{-1}\right[L{T}^{-1}]=[M^0{L}^0{T}^0]$ (Dimention less),

Option A