Question

A loop of area $0.5m^2$ is placed in a magnetic field of strength $2T$ in direction making an angle of ${30}^o$ with the field. The magnetic flux linked with the loop will be

• A. $\frac{1}{2}Wb$
• B. $\sqrt{\frac{3}{2}}Wb$
• C. $2Wb$
• D. $\frac{\sqrt{3}}{2}Wb$

Answer 1

The correct option is D $\frac{\sqrt{3}}{2}Wb$

Magnetic flux linked with an area is given by
${\varphi }_B=\int \overrightarrow{B.}\overrightarrow{dS}$
Here field is uniform therefore, ${\varphi }_B=BS\cos \theta$
${\varphi }_B=2\times 0.5\times \sqrt{3}/2$
${\varphi }_B=\sqrt{3}/2$.