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A square loop, carrying a steady current I, is placed in a horizontal plane near a long straight conductor carrying a steady current $I_1$ at a distance d from the conductor as shown in figure. The loop will experience
A
A net torque acting downward normal to the horizontal plane
B
A net attractive force towards the conductor
C
A net repulsive force away from the conductor
D
A net torque acting upward perpendicular to the horizontal plane
Detailed Solution
The field of the long wire, $B = \frac{\mu_0I_1}{2\pi r}$, decreases with distance r from the wire.
The two sides of the loop perpendicular to the wire carry opposite currents at the same set of distances, so the forces on them are equal and opposite and cancel.
In the figure, the side of the loop nearer to the wire carries current in the same direction as $I_1$; parallel currents attract, so this side is pulled towards the wire with force $\frac{\mu_0I_1Il}{2\pi d}$.
The far side carries current in the opposite direction and is repelled, but it is at a larger distance (d + l), so this force is smaller.
The net force is therefore towards the wire; all forces lie in the plane of the loop and act along the same line, so there is no net torque.
Hence the loop experiences a net attractive force towards the conductor.
The two sides of the loop perpendicular to the wire carry opposite currents at the same set of distances, so the forces on them are equal and opposite and cancel.
In the figure, the side of the loop nearer to the wire carries current in the same direction as $I_1$; parallel currents attract, so this side is pulled towards the wire with force $\frac{\mu_0I_1Il}{2\pi d}$.
The far side carries current in the opposite direction and is repelled, but it is at a larger distance (d + l), so this force is smaller.
The net force is therefore towards the wire; all forces lie in the plane of the loop and act along the same line, so there is no net torque.
Hence the loop experiences a net attractive force towards the conductor.