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Question

# The magnetic field normal to the plane of a wire of n turns and radius r which carries a current i is measured on the axis of the coil at a small distance h from the centre of the coil. This is smaller than the magnetic field at the centre by the fraction

A
(2/3)r2/h2
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B
(3/2)r2/h2
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C
(2/3)h2/r2
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D
(3/2)h2/r2
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Solution

## The correct option is D (3/2)h2/r2Magnetic field at the centre of the coil, Bc=μoni2rMagnetic field at an axial point , B=μonir22(r2+h2)32For h<<r,B=μoni2r[1−32h2r2]Now fractional changeδ=Bc−BBc⟹δ=32h2r2

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