A circular coil of wire of radius r has n turns and carries a current I . The magnetic induction B at a point on the axis of the coil at a distance 3 r from its centre is

Step-by-step solution

Magnetic field on the axis current carrying circular coil, B= ₀ I r^2 n 2 (x^2+r^2 )^ 3 / 2 where, I= current in the coil, n= number of turns, r= radius of coil. and x= distance of the point of observation from centre of coil. Here, x= 3 r aligned B & = ₀ I r^2 n 2 [( 3 r)^2+r^2 ]^ 3 / 2 = ₀ I r^2 n 2 [3 r^2+r^2 ]^ 3 / 2 & = ₀ I T n 2 (4 r^2 )^ 3 / 2 = ₀ I r^2 n 2 [(2 r)^2 ]^ 3 / 2 = ₀ I r^2 n 2 8 r^3 = ₀ n I 16 r aligned