MHTCET 11 Apr 2026 Shift 1 Paper

Concept:With a fixed wire length, increasing the number of turns reduces the area of each turn, which affects the net torque.Explanation:The torque on a coil in a magnetic field $B$ is:$$\tau = N i A B \sin\theta$$where $N$ is the number of turns, $A$ is the area of each turn, $i$ is the current, and $\theta$ is the angle between the coil's normal and $B$.Since the total wire length $L$ is fixed, if the coil has $N$ turns, each turn is a circle of radius $r$:$$L = N(2\pi r)$$$$r = \frac{L}{2\pi N}$$The area of each turn is:$$A = \pi r^2 = \pi\left(\frac{L}{2\pi N}\right)^2 = \frac{L^2}{4\pi N^2}$$Substituting $A$ into the torque equation:$$\tau = N i B \sin\theta \times \frac{L^2}{4\pi N^2} = \frac{i B L^2 \sin\theta}{4\pi N}$$Thus, torque is inversely proportional to the number of turns:$$\tau \propto \frac{1}{N}$$Therefore, torque is maximum when $N$ is minimum.The smallest possible number of turns is $N = 1$.Answer:The torque is maximum when the number of turns is $1$.Correct option: A. 1.