16.(a) For a circular coil of radius R and N turns carrying current I, the magnitude of the magnetic field at a point on its axis at a distance x from its centre is given by,

         B = \frac{\mu _0 IR^2N}{2 ( x^2 + R^2 )^{3/2}} 

Show that this reduces to the familiar result for the field at the centre of the coil.

Answers (1)
S Sayak

For a circular coil of radius R and N turns carrying current I, the magnitude of the magnetic field at a point on its axis at a distance x from its centre is given by,

         B = \frac{\mu _0 IR^2N}{2 ( x^2 + R^2 )^{3/2}} 

For finding the field at the centre of coil we put x=0 and get the familiar result

B = \frac{\mu _0 IN}{2R}

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