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 $S =\frac{1}{\text { meter }} \times \frac{q}{\text { time }} \times \frac{\text { Force }}{q}$
$=\frac{\text { Force }}{\text { meter }-\text { time }}$