First slide

Magnetism

Question

The ratio of magnetic inductions on the axial line of a bar magnet at distances 10cm and 15cm from the center of the magnet are in the ratio 5.8: 1. The distance between the two poles of the magnet is

Difficult

A

24cm
B

12cm
C

2.4cm
D

1.2cm

Solution

$F o r l o n g b a r m a g n e t, B_{a x i a l} = \frac{μ_{o}}{4 π} \frac{2 M d}{{(d^{2} - l^{2})}^{2}}$
$\Rightarrow B \propto \frac{d}{{(d^{2} - l^{2})}^{2}}$
$\Rightarrow \frac{5.8}{1} = \frac{10}{15} {[\frac{15^{2} - l^{2}}{10^{2} - l^{2}}]}^{2}$
$\Rightarrow 8.7 {(10^{2} - l^{2})}^{2} = {(15^{2} - l^{2})}^{2} \Rightarrow 2.95 (100 - l^{2}) = (225 - l^{2})$
$\Rightarrow l^{2} = \frac{295 - 225}{2.95 - 1} = \frac{70}{1.95} ≃ 36 \Rightarrow l = 6$
$\Rightarrow D i s \tan c e b e t w e e n t w o p o l e s = 2 l = 12 c m$

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