Write the expression for the magnetic moment due to a planar square loop of side ‘l’ carrying a steady current I in a vector form.

In the given figure this loop is placed in a horizontal plane near a long straight conductor carrying a steady current I₁ at a distance l as shown. Give reason to explain that the loop will experience a net force but no torque. Write the expression for this force acting on the loop.

Hi Sanal!

The magnetic moment , where, is the unit vector along the normal to the surface of the loop.

The attractive force per unit length of the loop is

The repulsive force per unit length of the loop is

Net force = F_net= F_a-F_r

The net force acting on the loop is not zero, because the attractive force is greater than the repulsive force.

The torque on the loop is given by,

, where, A is the area vector of the loop and  is the angle between the area vector and the magnetic field.

Here, the area vector is parallel to the magnetic field, so =0⁰. Therefore,

The torque acting on the loop is zero.

Cheers!!