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Figure shows a coil of radius 2 cm concentric with a coil of radius 7 cm. Each coil has 1000 turns' With a current of 5 amp in larger coil, find the current needed in the smaller coil to give the total magnetic field at the centre equal to 2 mT

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a

0.793A

b

1 44A

c

2.88A

d

3.4A

answer is A.

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Detailed Solution

Let B1 and B2 be the magnetic fields at centres due to bigger and smaller coils. Therefore,B1=μ0ni12r1=4π×10−7×100×52×0.07=4.49mTand B2=μ0ni22r2=4π×10−7×100×i22×0⋅02 B1−B2=2 or B2=4.49−2=2.49mT∴ 2⋅49=4π×10−7×100×i22×0⋅02i2=0.793amp

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Figure shows a coil of radius 2 cm concentric with a coil of radius 7 cm. Each coil has 1000 turns' With a current of 5 amp in larger coil, find the current needed in the smaller coil to give the total magnetic field at the centre equal to 2 mT