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) ?

(B) $\frac{\text { Force }}{\text { Length × Time }}$; (D) $\frac{\text { Power }}{\text { Area }}$

(A) $\frac{\text { Energy }}{\text { charge × current }}$

(C) $\frac{\text { Energy }}{\text { Volume }}$

JEE Advanced · 2021 · 03 Oct 2021 · Paper 2 · Units & Measurement

A physical quantity

S

is defined as

S = (E \times B) / μ_{0}

, where

E

is electric field,

B

is magnetic field and

μ_{0}

is the permeability of free space. The dimensions of

S

are the same as the dimensions of which of the following quantity (ies) ?

Answer: (B), (D)

The quantity

S = (E \times B) / μ_{0}

is the Poynting vector, which represents the energy flux (power per unit area) in an electromagnetic wave.

Dimensions of

S

[S] = \frac{[ E ] [ B ]}{[ μ _{0} ]} = \frac{Power}{Area} = \frac{Energy}{Area \times Time}

Checking each option:

(A)

\frac{Energy}{charge \times current} = \frac{Energy}{charge \times charge/time} = \frac{Energy \times time}{charge ^{2}}

✗

(B)

\frac{Force}{Length \times Time} = \frac{Energy/Length}{Length \times Time} = \frac{Energy}{Length ^{2} \times Time} = \frac{Power}{Area}

✓

(C)

\frac{Energy}{Volume} = \frac{Energy}{Length ^{3}}

✗

(D)

\frac{Power}{Area}

✓

Correct answers: (B) and (D)

JEE Advanced · 2021 · 03 Oct 2021 · Paper 2 · One or more correct options