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A physical quantity $\vec{S}$ is defined as $\vec{S}=(\vec{E} \times \vec{B}) / \mu_0$, where $\vec{E}$ is electric field, $\vec{B}$ is magnetic field and $\mu_0$ is the permeability of free space. The dimensions of $\vec{S}$ are the same as the dimensions of which of the following quantity (ies)?
$(A)$ $\frac{\text { Energy }}{\text { charge } \times \text { current }}$
$(B)$ $\frac{\text { Force }}{\text { Length } \times \text { Time }}$
$(C)$ $\frac{\text { Energy }}{\text { Volume }}$
$(D)$ $\frac{\text { Power }}{\text { Area }}$
$A,B,C$
$A,B,D$
$A,B$
$B,D$
Solution
$\overrightarrow{ S }=[\overrightarrow{ E } \times \overrightarrow{ B }] \frac{1}{\mu_0}$
$S$ is pointing vector denotes flow of energy per unit area per unit time
$\overrightarrow{ S }=\frac{\text { watt }}{ m ^2}$
Hence $B, D$ are correct
