A copper wire is wound on a wooden frame, whose shape is that of an… | JEE Main 2019 (11 Jan, Shift 2)

Q75JEE Main 2019 · 11 JAN · SHIFT 2Medium

Self-Inductance & Energy

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:

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Answer: (d)

The wire is wound around the bars of the frame, like a solenoid bent along the triangle: $L = \mu_0 n^2 A\, l$ .
Here $A$ is the cross-section of the frame bar (unchanged) and $l$ is the total wound length (perimeter).
With $n$ fixed, $L \propto l$ ; each side $\times 3$ gives $l \times 3$ .
So the answer is (d) increases by a factor of 3.

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Self-Inductance & Energy question from JEE Main 2019 (11 Jan, Shift 2)

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