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Question

A square wire loop of 10.0 cm side lies at right angles to a uniform magnetic field of 20 T. A 10 V light bulb is in a series with the loop as shown in the fig. The magnetic field is decreasing steadily to zero over a time interval Δt. The bulb will shine with full brightness if Δt is equal to


A
20 ms
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B
0.02 ms
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C
2 ms
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D
0.2 ms
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Solution

The correct option is A 20 ms
The bulb will shine with the full brightness when the emf induced in the loop is equal to the voltage rating of the bulb.


Emf induced, E=10 V

10=ΔϕΔt=|ϕ2ϕ1|Δt

Here, ϕ1=BA=20×(0.1)2=0.2 Wb

ϕ2=0 Wb [B=0]

10=|00.2|Δt

Δt=0.210=0.02 s=20 ms

Hence, (A) is the correct answer.

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