Question

Four wires, each of length 2 m, are bent into four loops P, Q, R and S and then suspended in uniform magnetic field. If the same current is passed in each, then in which loop will the torque be maximum?

A. P
B. Q
C. R
D. S

Answer 1

Hint: The given question is based on torque experienced on a current carrying loop placed in a uniform magnetic field or a magnetic dipole in a uniform magnetic field. The value of the torque is given by $\tau = iAB\sin \theta = MB\sin \theta $ , where $A$ is the area of the loop and $M$ is the magnetic dipole moment.

Complete answer:
Torque in a current carrying loop placed in a uniform magnetic field is given by:
$\tau = iAB\sin \theta $ … (1)
Where
$i$ is the current flowing through the loop,
$A$ is the area of the loop,
$B$ is the intensity of the magnetic field and
$\theta $ is the angle between the magnetic field and the axis of the loop.

For the given four loops, the only variable having a different value, to calculate the torque, is $A$ , that is, the area of the loop. It is given that each of the wires are of same length, 2m. For same perimeter, among the given figures, area of a circle will be maximum. Hence, when substituting all the values in (1), the value of the torque calculated will be maximum for the loop S, as its area is the most.

Thus, the correct option is D.

Note: In the above question, it is important to note that a circle is the most systematic shape for a given perimeter. Among all the shapes having the same perimeter, a circle is the one that will be having the maximum area.