Question

A conducting circular loop of radius $r$ carries a constant current $i$. It is placed in a uniform magnetic field ${\overline{B}}_o$ such that ${\overline{B}}_o$ is perpendicular to the plane of the loop. The magnetic force acting on the loop is

• A. $ir{\overline{B}}_o$
• B. $2\pi ri{\overline{B}}_o$
• C. $0$
• D. $\pi ri{\overline{B}}_o$

Answer 1

The correct option is C $0$

The direction of magnetic force acting on a small current carrying element is given by $\overrightarrow{dF}=i(\overrightarrow{dl}\times \overrightarrow{B})$

$⟹\overrightarrow{F}=\oint i(\overrightarrow{dl}\times \overrightarrow{B})$

Since the vectors $\overrightarrow{dl}$ form a closed loop with angle between $\overrightarrow{dl}$ and $\overrightarrow{B}$ equal to ${90}^{\circ }$, the net force is zero.