A circular current carrying coil has radius R . The magnetic induction at the centre of the coil is B _ C . The magnetic induction of the coil at a distance 3 R from the centre along the axis is B _ A . The ratio B _ A : B _ C is

Step-by-step solution

Magnetic Induction of Current carrying coil at its centre: B _ c = _ o I 2 R Magnetic Induction of Current carrying coil at distance r : B _ A = ₀ IR ^2 2 ( R ^2+ r ^2 )^ 3 / 2 Given r= 3 R B_A= ₀ I^2 2 (R^2+( 3 R)^2 )^ 3 / 2 Ratio of B _ A to B _ C is B _ A B _ C = ₀ IR ^2 2 ( R ^2+( 3 R )^2 )^ 3 / 2 ₀ I 2 R = ₀ IR ^2 2 (4 R ^2 )^ 3 / 2 2 R ₀ I B _ A B _ C = 1 8