Question

A wire of length \(L\) is bent in the form of a circular coil and current '\(i\)' is passed through it. This coil is kept in magnetic field. The torque acting on the coil will be maximum, when the number of turns is ___

• A. \(1\)
• B. \(2\)
• C. \(4\)
• D. As large as possible

Hint:

Radius shrinks as turns increase, so area falls faster than $N$ rises.

Answer 1

The Correct Option is A

Step 1: Relation
The wire of length \(L\) gives \(N\) turns of radius \(r\): \(L=N\cdot2\pi r\), so \(r=\frac{L}{2\pi N}\).

Step 2: Torque
\(\tau=NiAB=Ni\pi r^2B=Ni\pi B\frac{L^2}{4\pi^2N^2}=\frac{iBL^2}{4\pi N}\).

Step 3: Maximise
\(\tau\propto\frac1N\), so it is largest for the smallest \(N\), that is \(N=1\). Option (A).

Final Answer:
The torque is maximum for \(N=1\), option (A). \[ \boxed{\text{(A) }1} \]