Question

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. $\frac{\text{ Force }}{\text{ Lenght }\times \text{ Time }}$
• C. $\frac{\text{ Energy }}{\text{ Volume }}$
• D. $\frac{\text{ Power }}{\text{ Area }}$

Answer 1

Answer: (B), (D)

$\vec{S}=\vec{E}\times \vec{B}$
Method - 1:
$\vec{S}$ is pointing vector which is defined as energy flowing per unit area in unit time.
S.I. unit of $S$ is Watt $/m^2$.
Method 2:
$\because B={\mu }_{0}ni\Rightarrow \frac{1}{{\mu }_0}=\frac{ni}{B}$
$S=\frac{1}{{\mu }_0}EB\cos \theta =niE\cos \theta$
S.I. unit of $S=\frac{1}{\text{ meter }}\times \frac{q}{\text{ time }}\times \frac{\text{ Force }}{q}$
$=\frac{\text{ Force }}{\text{ meter }-\text{ time }}$