Question

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

• A. 5 cm
• B. 25 cm
• C. 10 cm
• D. 20 cm

Answer 1

Answer: (C)

10 cm

Answer 2

$\frac { B _ { 1 } } { B _ { 2 } } = \frac { d _ { 1 } } { d _ { 2 } } \left( \frac { d _ { 2 } ^ { 2 } - l ^ { 2 } } { d _ { 1 } ^ { 2 } - l ^ { 2 } } \right) ^ { 2 } \Rightarrow \frac { 12.5 } { 1 } = \frac { 10 } { 20 } \left( \frac { 400 - l ^ { 2 } } { 100 - l ^ { 2 } } \right) ^ { 2 }$

$\Rightarrow l = 5 \mathrm {~cm}$

Hence length of magnet