A physical quantity vec S is defined as vec S =(vec E × vec B ) / μ 0 , where vec E is electric field, vec B is magnetic field and μ 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)?

Physics · Units, Dimensions & Error Analysis

JEE Advanced 2021 — Paper 2 — Question 4

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)?

Option A:
$\frac{\text { Energy }}{\text { Charge } \times \text { Current }}$
Option B:
$\frac{\text { Force }}{\text { Lenght } \times \text { Time }}$
Correct
Option C:
$\frac{\text { Energy }}{\text { Volume }}$
Option D:
$\frac{\text { Power }}{\text { Area }}$
Correct

Answer: B, D

Step-by-step solution

$\vec{S}=\vec{E} \times \vec{B}$ 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 $/ \mathrm{m}^{2}$ . $\because \quad B=\mu_{0} n i \Rightarrow \frac{1}{\mu_{0}}=\frac{n i}{B}$

$\mathrm{S}=\frac{1}{\mu_{0}} \mathrm{~EB} \cos \theta=n i E \cos \theta$

S.I. unit of $S=\frac{1}{\text { meter }} \times \frac{\mathrm{q}}{\text { time }} \times \frac{\text { Force }}{q}=\frac{\text { Force }}{\text { meter }- \text { time }}$

Answer key and solution verified before publishing.

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Exam: JEE Advanced 2021
Paper: Paper 2
Subject: Physics
Chapter: Units, Dimensions & Error Analysis
Topic: Units and Dimensions Analysis