JEE Main 2026 · 2 Apr · Shift 1 · Physics Q38

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PhysicsSingle correct+4 / -1Question 38 of 75

When a coil is placed in a time dependent magnetic field the power dissipated in it is $P$ . The number of turns, area of the coil and radius of the coil wire are $N$ , $A$ and $r$ respectively. For a second coils number of turns, area of the coil and radius of the coil wire are $2N$ , $2A$ and $3r$ respectively. When the first coil is replaced with second coil the power dissipated in it is $\sqrt2\,\alpha P$ . The value of $\alpha$ is ________.

128\sqrt2

Answer and worked solution

Official answer: A

Power. $P=\dfrac{\varepsilon^2}R$ , where $\varepsilon\propto NA$ (same $dB/dt$ ).

Resistance. The wire length is $\propto N\sqrt A$ (N turns of perimeter $\propto\sqrt A$ ) and its cross-section $\propto r^2$ , so $R\propto\dfrac{N\sqrt A}{r^2}$ .

Scaling. $P\propto\dfrac{N^2A^2r^2}{N\sqrt A}=NA^{3/2}r^2$ . For the second coil: $2\cdot2^{3/2}\cdot9=36\sqrt2$ , so $\alpha=36$ .

(A)

Topics:Faraday's and Lenz's laws Ohm's law and resistivity

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JEE Main 2026 · 2 Apr · Shift 1, Physics question 38