Q 12-06-139JEE MainJEE Main 2019 (11 Jan, Shift 2)Medium
A copper wire is wound on a wooden frame, whose shape is that of an equilateral triangle. If the linear dimension of each side of the frame is increased by a factor of $3$, keeping the number of turns of the coil per unit length of the frame the same, then the self inductance of the coil:
Answer: (C) increases by a factor of $3$
The wire is wound around the frame like a toroid, so the cross-sectional area $A$ of each turn is that of the frame's bar, which does not change. For such a winding of total length $l$ with $n$ turns per unit length:
$$L = \mu_0n^2Al$$
With $n$ and $A$ fixed, $L \propto l$. Tripling each side triples the length of the frame, so the self inductance increases by a factor of $3$.
Solution by Sreeraj P, M.Sc Physics