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

5 cm

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25 cm

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10 cm

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20 cm

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Solution

The correct option is C 10 cm
$\frac{B_{1}}{B_{2}} = \frac{d_{1}}{d_{2}} {(\frac{d_{2}^{2} - l^{2}}{d_{1}^{2} - l^{2}})}^{2} \Rightarrow \frac{12.5}{1} = \frac{10}{20} {(\frac{100 - l^{2}}{100 - l^{2}})}^{2}$
$\Rightarrow l = 5 c m$
Hence length of magnet =2l =10 cm

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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

The correct option is C 10 cmB1B2=d1d2(d22−l2d21−l2)2⇒12.51=1020(100−l2100−l2)2 ⇒l=5cm Hence length of magnet =2l =10 cm

The correct option is C 10 cm
$\frac{B_{1}}{B_{2}} = \frac{d_{1}}{d_{2}} {(\frac{d_{2}^{2} - l^{2}}{d_{1}^{2} - l^{2}})}^{2} \Rightarrow \frac{12.5}{1} = \frac{10}{20} {(\frac{100 - l^{2}}{100 - l^{2}})}^{2}$
$\Rightarrow l = 5 c m$
Hence length of magnet =2l =10 cm