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Question

Two circular coils of radii 5cm and 10cm carry equal currents of 2A. The coils have 50 and 100 turns respectively, and are placed in such a way that their planes as well as their centers coincide. Magnitude of magnetic field at the common center of coils is

A
8π×106 T if current in the coils are in the same sense
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B
4π×106 T if current in the coils are in the opposite sense
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C
zero if current in the coils are in opposite sense
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D
8π×106 T if current in the coils are in the opposite sense
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Solution

The correct options are
A 8π×106 T if current in the coils are in the same sense
D zero if current in the coils are in opposite sense
B1=n1mu0i12r1

B2=n2mu0i22r2

If currents are in the same sense:

B=B1+B2=μ0i2(n1r1+n2r2)=4π×107×22×(550+10100)×1102=8π×106T

If currents are in the opposite sense

B=B1+B2=μ0i2(n1r1n2r2)=4π×107×22×(55010100)×1102=0

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