Question

Assertion: No net force acts on a rectangular coil carrying a steady current when suspended freely in a uniform magnetic field.
Reason: Force on a coil in a magnetic field is always non-zero.
A. If both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
B. If both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
C. If Assertion is correct but Reason is incorrect.
D. If Assertion is incorrect but Reason is correct.

Answer 1

Hint: A current-carrying conductor when placed in a magnetic field experiences a force which is perpendicular to both the magnetic field and to the direction of the current flow. If we arrange the thumb, the center finger, and the forefinger of the left hand at right angles to each other, then the thumb points towards the direction of the magnetic force, the center finger gives the direction of current and the forefinger points in the direction of a magnetic field.

Complete answer:
Let a rectangular coil having cross sectional area, \[A\] is lying in a uniform magnetic field \[B\] in such a way that the plane of the coil makes an angle \[\theta \] with the magnetic field. The direction of current in the four arms of the coil will be in cyclic manner, say from point $P$ to $Q$ to $R$ to $S$; $PQRS$ being the four corners of the coil. Now two parallel arms say $PS$ and $QR$ will stay perpendicular to the magnetic field, while the other two arms, $PQ$ and $RS$ will be tilted.

When we apply the Fleming’s rule on the arms of the coil then we will find the direction of force on each arm. The forces on the parallel pairs will be opposite in direction (by Fleming’s rule) but equal in magnitude (length of arms are equal, the angles made by them with the field are same and the magnetic field is uniform). Hence the forces will cancel out each other, therefore the net force on the coil will be zero, but a torque will exist. Therefore the Assertion is correct but the reason is incorrect.

Hence, the correct answer is option C.

Note:The uniformity of the magnetic field defines whether the force on parallel pairs will cancel out each other or not. If the field is not uniform then we can calculate different magnitudes of force on each arm. The torque depends on the angle \[\theta \], if the coil is perpendicular to the magnetic field then the torque is zero or minimum. And if it is parallel then the torque is maximum.