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The distance of two points on the axis of a magnet from its center 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

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20 cm

25 cm

10 cm

5 cm

answer is C.

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Detailed Solution

$\frac{B_{1}}{B_{2}} = \frac{d_{1}}{d_{2}} {(\frac{d_{2}^{2} - l^{2}}{d_{1}^{2} - l^{2}})}^{2} \Rightarrow \frac{12 .5}{1} = \frac{10}{20} {(\frac{400 - l^{2}}{100 - l^{2}})}^{2}$

$\Rightarrow l = 5 cm$

Hence length of magnet $= 2 l = 10 cm$

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