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Question

A circular loop of radius r carries a current i. How should a long, straight wire carrying a current, 4i be placed in the plane of the circle so that the magnetic field at the centre becomes zero ?

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Solution

Magnetic field due to loop at its centre

B=μ0i2r

To vanish above magnetic field we place a straight wire of 4i current at a distance x such that their magnetic fields directions be opposite.

Thus μ0i2r=μ0 4i2πx

x=8x2π=4rπ

i.e wire is placed 4rπ from the centre of the loop


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