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Question

A square wire loop of 10 cm side lies at right angles to a uniform magnetic field of 20 T in vertically downwards direction. 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
Area of the square loop is
S=100 cm2=102 m2
Taking direction of area along direction of B, (cosθ=cos0=1)
ϕ=BScos0=BS
Rate of change of flux linked with loop is,
ΔϕΔt=S(ΔBΔt) ...(i)
induced emf across loop is,
ε=ΔϕΔt ...(ii)
The bulb will shine with full brightness if induced emf in loop is equal to 10 V.
From Eq (i) & (ii),
10=S(ΔBΔt)
10=102×(020Δt)
Δt=20×103 s
Δt=20 ms

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