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Magnetic field due to current element

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Question

Two circular coils X and Y, having equal number of turns and carrying currents in the same sense, subtend same solid angle at point O. If the smaller coil X is midway between O and Y and if we represent the magnetic induction due to bigger coil Y at O as By and that due to smaller coil Y at O as Bx, then find the ratio Bx/By.

 

Moderate
Solution

By=μ04π2πI(2r)2(2r)2+(2d)23/2,Bx=μ04π2πIr2r2+d23/2  solve to get BxBy=2


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