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Question

# Two circular coils of radii 5 cm and 10 cm carry equal current of 2 A. The coils have 50 and 100 turns respectively and are placed in such a way that their planes as well as their centre coincide magnitude of magnetic field at the common centre of the coil is

A
8π×104 T, if current in the coils are in same sense
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B
4π×104 T, if current in the coil are in opposite sense.
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C
zero, if current in the coils are in opposite sense
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D
8π×104 T, if current in the coil are in opposite sense
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Solution

## The correct option is C zero, if current in the coils are in opposite senseGiven: r1=5 cm, r2=10 cm, N1=50 N2=100 I1=I2=2 A When current flows in same direction BNet=N1μ0I12πr1+μ0N2I22πr2 ⇒BNet=μ0π[N1r1+N2r2]=4π×10−7π[505×10−2+10010×10−2]=8π×10−4 T When current flows in opposite direction BNet=N1μ0I12πr1−μ0N2I22πr2=0 a,c are correct

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