A current carrying circular coil of radius R has a point P situated on its axis at a distance x from its centre O of the coil. The magnetic induction at point P is ( 1 8 )^ th of magnetic field at its centre O. The value of x is

Step-by-step solution

Magnetic field on the axis of a circular coil, at a location x away from the center of the coil is given by, B= ₀ I R^2 2 (R^2+x^2 )^ 3 2 For, x=0 the induction at the centre of the coil is B₀= ( ₀ I 2 R ) aligned & 1 8 ( ₀ I 2 R )= ₀ I R^2 2 (R^2+x^2 )^ 3 2 & (2 R)^3= (R^2+x^2 )^ 3 2 & (2 R)= (R^2+x^2 )^ 1 2 & (2 R)^2= (R^2+x^2 ) & x= 3 R aligned