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×10−6 T if current in the coils are in the same sense D zero if current in the coils are in opposite senseB1=n1mu0i12r1B2=n2mu0i22r2If currents are in the same sense:B=B1+B2=μ0i2(n1r1+n2r2)=4π×10−7×22×(550+10100)×110−2=8π×10−6TIf currents are in the opposite senseB=B1+B2=μ0i2(n1r1−n2r2)=4π×10−7×22×(550−10100)×110−2=0

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