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Question

A wire 40 cm long is bent into a rectangular frame 15 cm×5 cm and placed perpendicular in a magnetic field intensity of 0.8 T . The frame is changed into a square frame and the field is increased to 1.4 T in a time interval of 0.5 s. The e.m.f induced in the frame is ________.

A
1.6×102 V
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B
1.6×103 V
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C
1.6×104 V
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D
1.6×105 V
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Solution

The correct option is A 1.6×102 V
The emf induced is given by

emf=Δ(BA)t

where B is the magnetic field in Tesla.
A is the area of the frame and t is the time period.

Given:
Initial area of the frameA1=15×5=75 cm2
A2=a2|4a=40=10×10 a=10 cmA2=100 cm2
where A2 is the new area or the final area.
e=(B2A2B1A1)t=(1.4×1000.8×75)×1040.5
=1.6×102 V

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