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Question

A long solenoid of diameter 0.1 m has 2×104 turns per meter. At the centre of the solenoid, a coil of 100 turns and radius 0.01 m is placed with its axis coinciding with the solenoid axis. The current in the solenoid reduces at a constant rate to 0 A from 4 A in 0.05 s. If the resistance of the coil is 10π2 Ω, the total charge flowing through the coil during this time is

A
32π μC
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B
64π μC
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C
8π μC
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D
16π μC
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Solution

The correct option is A 32π μC
By Lenz's law
e=NdϕdtDividing by R on both side(eR=(NRdϕdt where, dq=NRdϕΔQ=N(Δϕ)RΔQ=(Δϕtotal)R =NΔ(BA)R = NAΔBR =NARμ0ΔIRΔQ = 2×104×π×(0.01)2×100×4π×107×410π2 = 32 μC

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