Question

The magnetic field in a certain region is given by $\overrightarrow{B}=(4\hat{i}-\hat{k})\text{T}$. How much magnetic flux passes through the loop of area $0.1{\text{m}}^2$ in this region, if the loop lies flat in $xy$ plane?

• A. $5\text{Wb}$
• B. $2.5\text{Wb}$
• C. $1\text{Wb}$
• D. $0.1\text{Wb}$

Answer 1

The correct option is D $0.1\text{Wb}$

$\overrightarrow{B}=(4\hat{i}-\hat{k})\text{T}$

$A=0.1m^2$

Since, the loop lies in $x-y$ plane, its area vector must lie along $z-$axis.

$\therefore \overrightarrow{A}=(\pm 0.1\hat{k}){\text{m}}^2$

Flux linked with the loop is,

$|\varphi |=|\overrightarrow{B}\cdot \overrightarrow{A}|=\left|\right(4\hat{i}-\hat{k})\cdot (0.1\hat{k}\left)\right|$

$\therefore |\varphi |=0.1\text{Wb}$

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

Why this Question? Note: Always remember that the area vector is perpendicular to the plane of the loop.