The distance of two points on the axis of a magnet from its centre is 10 cm and 20 cm respectively. The ratio of magnetic intensity at these points is 12 . 5 : 1 . The length of the magnet will be

Step-by-step solution

The magnetic field on the axis of a bar magnet of length 2 l , having a pole strength m , at a distance d is B = μ 0 4 π m d - l 2 - μ 0 4 π m d + l 2 B = μ 0 m 4 π d + l 2 - d - l 2 d 2 - l 2 2 = μ 0 mld π d 2 - l 2 2 ⇒ B 1 B 2 =   d 1 d 2   d 2 2 - l 2 d 1 2 - l 2 2 ⇒ 12 .5 1 = 10 20   400 - l 2 100 - l 2 2 ⇒ l = 5 cm Hence, length of magnet = 2 l = 10 cm