Question

A loop of wire is placed in a magnetic field $\overrightarrow{B}=0.3\hat{j}\text{T}$. Find the flux through the loop, if the area vector is $\overrightarrow{A}=(2\hat{i}+5\hat{j}-3\hat{k}){\text{m}}^2$

• A. $1\text{Wb}$
• B. $1.5\text{Wb}$
• C. $2\text{Wb}$
• D. $2.5\text{Wb}$

Answer 1

The correct option is B $1.5\text{Wb}$

Given, $\overrightarrow{B}=0.3\hat{j}\text{T}$

$\overrightarrow{A}=(2\hat{i}+5\hat{j}-3\hat{k}){\text{m}}^2$

Flux linked with the surface is given by,

$\varphi =\overrightarrow{B}.\overrightarrow{A}$

$\varphi =\left(0.3\hat{j}\right).(2\hat{i}+5\hat{j}-3\hat{k})$

$\varphi =0+0.3\times 5-0$

$\Rightarrow \varphi =1.5\text{Wb}$

Hence, option ($B$) is the correct answer.

Why this Question? Note: The magnetic flux is a measure of number of magnetic field lines crossing per unit area. It is given by, $\varphi =\overrightarrow{B}.\overrightarrow{A}$