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Question

A long straight wire is parallel to one edge of the loop as shown in the figure. If the current in the long wire varies with time as I=I0etτ, what will be the induced emf in the loop ?

A
μ0bIπτln(d+ad)
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B
μ0bI2πτln(d+aa)
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C
2μ0bIπτln(d+aa)
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D
μ0bIπτln(dd+a)
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Solution

The correct option is B μ0bI2πτln(d+aa)
The magnetic field at a distance x from the wire is B=μ0I2πx
The flux due to the magnetic field in the strip of thickness dx and length b is B.b.dx
Hence the total magnetic flux in the loop is
dϕ=a+ddμ0I2πx.b.dx
ϕ=μ0Ib2πln(d+aa)
E=dϕdt=μ0I0etτb2πτln(d+aa)
E=μ0Ib2πτln(d+aa)

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