Question

A current $i$ is flowing in a circular conductor of radius $r$, it is lying in a uniform magnetic field $B$ such that its plane is normal to $B$. The magnetic force acting on the loop will be_

• A. $zero$
• B. $\pi irB$
• C. $2\pi irB$
• D. $irB$

Answer 1

Answer: (A)

$zero$

Lets consider a small arc of length $dl$ of the circular loop

The magnetic force acting on the loop will be,

$\overrightarrow{F}=i(d\overrightarrow{l}\times \overrightarrow{B})$ .. . . .. . . .. (1)

the force acting towards the center.

When the magnetic field $B$ is perpendicular to the $dl$, the angle between them is ${90}^0$.

$\theta ={90}^0$

From equation (1),

$\overrightarrow{F}=i|d\overrightarrow{l}||\overrightarrow{B}|sin\theta =idlB$

But the similar element of arc is opposite to the consider arc, so the current is also in the opposite direction and the force acting on the loop is now towards outward, both force cancel each other and the net force acting on the loop will be zero.

The correct option is A.