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Question

A very long solenoid of radius R is carrying current I(t)=kteαt(k>0), as a function of time (t0). Counterclockwise current is taken to be positive. A circular conducting coil of radius 2R is placed in the equatorial plane of the solenoid and concentric with the solenoid. The current induced in the outer coil is correctly depicted, as a function of time, by-

A
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C
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D
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Solution

The correct option is C
Flux linked with the coil is,

ϕ=BA=(μ0nI)A=μ0n(kteαt)A

e=dϕdt=μ0nAkddt(teαt)

=μ0nAk[teαt(α)+eαt×1]

=μ0nAk[eαt(1αt)]

iind=eResistance=μ0nAkResistance[eαt(1αt)]

At t=0, ive

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, (A) is the correct answer.

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