Magnetic fields at two points on the axis of a circular coil at a distance of 0 . 05 m and 0 . 2 m from the centre are in the ratio 8 : 1 . The radius of coil is _______ .

Step-by-step solution

We know, the magnetic field on the axis of a current carrying circular ring is given by B = μ 0 4 π 2 N I A R 2 + x 2 3 / 2 ∴     B 1   B 2 = 8 1 = R 2 + 0 . 2 2 R 2 + 0 . 05 2 3 / 2 4 R 2 + 0 . 05 2 = R 2 + 0 . 2 2 4 R 2 - R 2 = 0 . 2 2 - 4 × 0 . 05 2 4 R 2 - R 2 = 0 . 2 2 - 0 . 1 2 3 R 2 = 0 . 3 × 0 . 1 R 2 = 0 . 1 2 ⇒ R = 0 . 1