An insulated copper wire of 100 turns is wrapped around a wooden… | JEE Main 2023 (13 Apr, Shift 2)

Q51JEE Main 2023 · 13 APR · SHIFT 2Medium

Magnetic Flux & Faraday's Law

An insulated copper wire of 100 turns is wrapped around a wooden cylindrical core of the cross- sectional area $24\text{ cm}^{2}$ . The two ends of the wire are connected to a resistor. The total resistance in the circuit is $12\ \Omega$ . If an externally applied uniform magnetic field in the core along its axis changes from $1.5\text{ T}$ in one direction to $1.5\text{ T}$ in the opposite direction, the charge flowing through a point in the circuit during the change of magnetic field will be ___________ $\text{mC}$ .

Numerical answer type. Work it out, then open the answer.

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Answer: 60

Field reverses, so $\Delta B = 3$ T and $\Delta\phi = NA\Delta B = 100 \times 24 \times 10^{-4} \times 3 = 0.72$ Wb.
$q = \frac{\Delta\phi}{R} = \frac{0.72}{12} = 0.06$ C
So the charge is $60$ mC.

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