Question

A square of side a metre lies in the YZ-palne in a region, where the magnetic field is given $B=B_0(3\hat{i}+3\hat{j}-4\hat{k})T$, where $B_0$ is constant. The magnitude flux passing through the square in Wb is:

• A. $2B_0{a}^2$
• B. $5B_0{a}^2$
• C. $3B_0{a}^2$
• D. $4B_0{a}^2$

Answer 1

The correct option is D $4B_0{a}^2$

$Given:$ $\overrightarrow{B}=B_0(3\hat{i}+3\hat{j}-4\hat{k})$

$Solution:$ We know that ;

$\mathrm{flux}\left(\varphi \right)=\overrightarrow{B}\cdot \overrightarrow{A}$

where $\overrightarrow{A}$ is area vector of the loop.

$\overrightarrow{A}$ is perpendicular to the plane of the loop.

so here $\overrightarrow{A}=A\hat{K}\mid =a^2\hat{k}$ as area $=a\times a=$

$a^2$

$So;\varphi =\overrightarrow{B}\cdot \overrightarrow{A}$

$=B_0(3\hat{i}+3\hat{j}-4\hat{k})\cdot \left(a^2\hat{k}\right)$

$\varphi =4B_0{a}^2$

$So,the$ $correct$ $option:D$