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Find the mutual inductance between two c...

Find the mutual inductance between two coaxial loops of radii R and r (R >> r) with separation between the centre x.

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Let a current i flows through coil of radius R. The field produced at the centre of the other coil is
`B= (mu_(0)i xx 2 xx pi R^(2))/(4pi ( R^(2)+ x^(2))^((3)/(2))`
As `R gt r`, this field can be assumed to be acting on the entire area of the smaller loop.
thus `phi = B xx A`
i.e `phi= (mu_(0)i xx 2 xx pi R^(2))/(4pi ( R^(2)+ x^(2))^((3)/(2)) xx pi r^(2)`
as `M= (phi)/(i)`
`implies M= (mu_(0)pi R^(2) r^(2))/( 2(R^(2)+ x^(2))^((3)/(2))`
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