Question

The dimensions of quantity $\frac{1}{{\mu }_0}(\overrightarrow{E}\times \overrightarrow{B})$ are:

$[{\mu }_0=$ permeability of free space, $E^1=$ electric field strength, $B^1=$ magnetic field induction $]$

• A. $\left[M{T}^{-3}\right]$
• B. $\left[M{L}^2{T}^{-3}\right]$
• C. $\left[M{L}^{-1}{T}^{-1}\right]$
• D. $\left[M{T}^{-3}{A}^2\right]$

Answer 1

The correct option is A $\left[M{T}^{-3}\right]$

$\frac{\left[E\right]\left[B\right]}{\left[{\mu }_0\right]}=\frac{\left[ML{T}^{-3}{I}^{-1}\right]\left[M{T}^{-2}{I}^{-1}\right]}{\left[ML{T}^{-2}{I}^{-2}\right]}$ $=M^{1+1-1}{L}^{1-1}{T}^{-3-2+2}{I}^{-1-1+2}$$=M{T}^{-3}$