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Question

A wire 88 cm long bent into a circular loop is placed perpendicular to the magnetic field of flux density 2.5Wbm2. Within 0.5 s, the loop is changed into a square and flux density is increased to 3.0Wbm2. The value of e.m.f. induced is

A
0.018V
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B
0.016V
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C
0.020V
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D
0.012V
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Solution

The correct option is A 0.018V
Answer is A.
The magnetic flux ϕ=B×A depends on the magnetic field, the area
of the loop, and their relative orientation.
In this case, the wire 88 cm long bent into a circular loop is placed perpendicular to the magnetic field and Within 0.5 s, the loop is changed into a square.
Magnetic Flux when in a circular loop:
Circumference of the loop = 2×3.14×r=88cm.
So, radius of the loop r = 14 cm.
Magnetic field ϕ=B×A=2.5×3.14×0.14×0.14=0.154Wb.
Magnetic Flux when in a square:
Circumference of the square = 4r=88cm
So, length of the side of the square is 884=22cm.
Magnetic feild ϕ=B×A=3×0.22×0.22=0.1452Wb.
The total induced emf is 0.1540.14520.5=0.018V.
Therefore, the value of e.m.f induced is 0.018 V.

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