JEE Main · 2019 · 11 Jan 2019 · Shift 2 · Electromagnetic Induction

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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 self inductance of the coil:

(A)decreases by a factor of 9
(B)increases by a factor of 27✓ Correct
(C)increases by a factor of 3
(D)decreases by a factor of $93$

Answer: (B)

Solution

Treating the coil as a solenoid,

L = μ_{0} n^{2} A l

with

n

the turns per unit length,

A

the cross-sectional area and

l

the length. Tripling every linear dimension while holding

n

fixed multiplies

A

9

and

l

3

, so

L

scales by

9 \times 3 = 27

; the self-inductance increases by a factor of

27

JEE Main · 2019 · 11 Jan 2019 · Shift 2 · Single correct option

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