The distance of two points on the axis of a magnet from its center is $10 c m$ and $20 c m$ respectively. The ratio of magnetic intensity at these points is $12.5 : 1$ The length of the magnet will be

5 c m

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25 c m

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10 c m

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20 c m

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Solution

The correct option is C $10 c m$
We know that on the axis of magnet,
$\frac{B_{1}}{B_{2}} = \frac{d_{1}}{d_{2}} \frac{({d_{2}}^{2} - l^{2})}{({d_{1}}^{2} - l^{2})}$

$\Rightarrow$ $\frac{12.5}{1} = \frac{10}{20} \frac{(400 - l^{2})}{(100 - l^{2})}$
$\Rightarrow$ $l = 5$

Hence the length of magnet = $2 l = 10 c m$

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The distance of two points on the axis of a magnet from its center is 10cm and 20cm 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 10cmWe know that on the axis of magnet,B1B2=d1d2(d22−l2)(d12−l2)⇒ 12.51=1020(400−l2)(100−l2)⇒ l=5Hence the length of magnet = 2l=10cm

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