A circular loop of radius a , carrying a current i , is situated in...

Consider a small current element $d\vec{l}$ on the circular loop.

The magnetic field $\vec{B}$ is radial and points outwards from the centre. The current element $d\vec{l}$ is tangential to the circular loop.

The angle between the current element $d\vec{l}$ and the magnetic field $\vec{B}$ is $90^{\circ}$.

The magnetic force on this small element is given by $d\vec{F} = i(d\vec{l} \times \vec{B})$.

The magnitude of this force is $dF = i B dl \sin(90^{\circ}) = i B dl$.

Using the right-hand rule, the direction of the cross product $d\vec{l} \times \vec{B}$ is into the plane of the figure for all elements along the loop.

Since the force on every element is directed into the plane of the figure, the total magnetic force is the sum of the magnitudes of these elemental forces.

$F = \int dF = \int i B dl = i B \int dl$

The total length of the loop is $\int dl = 2\pi a$.

Therefore, $F = i B (2\pi a) = 2\pi a i B$.

The net force is $2\pi a i B$, directed into the plane of the figure.

Answer: $2\pi a i B$, directed into the plane of the figure