Question

A physical quantity $\overrightarrow{S}$ is defined as $\overrightarrow{S}=(\overrightarrow{E}\times \overrightarrow{B})/{\mu }_0,$ where $\overrightarrow{E}$ is electric field, $\overrightarrow{B}$ is magnetic field and ${\mu }_0$ is the permeability of free space. The dimensions of $\overrightarrow{S}$ 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. $\frac{\text{Power}}{\text{Area}}$

Answer 1

Answer: (B), (D)

$\frac{\text{Power}}{\text{Area}}$

$\overrightarrow{S}=\frac{[\overrightarrow{E}\times \overrightarrow{B}]}{{\mu }_0}$

Here, $S$ is the Poynting vector which denotes flow of energy per unit area per unit time, which is energy flux or intensity.

$\therefore \overrightarrow{S}=\frac{\text{Energy}}{\text{Time-Area}}\text{or}\frac{\text{Force}}{\text{Time- Length}}$

So, unit of $\overrightarrow{S}$ is $\frac{\text{Watt}}{{\text{m}}^2}$.

And here, options $\left(\text{B}\right)$ and $\left(\text{D}\right)$ have same unit, so these two are the correct options.