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Question

A long solenoid of diameter 0.1 m has 2×104 turns per metre.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 10 π2Ω, the total charge flowing through the coil during this time is.

A
32 πμC
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B
16 μC
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C
32 μC
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D
16 πμC
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Solution

The correct option is B 32 μC
Given,

Number of turns, n=100

Radius, r=0.01m

Resistance, R=10π2Ω

As we know,

ϵ=Ndϕdt

=ϵR=NRdϕdt, ΔI=NRdϕdt

ΔΔt=NRΔϕΔtΔq=[NR(ΔϕΔt)]Δt

ve sign shoes that induced emf opposes the change in flux.

Δq=μ0niπr2R

Δq=4π×107×100×4×π×(0.01)210π2=32μC

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