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Question

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


A
5cm
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B
25cm
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C
10cm
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D
20cm
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Solution

The correct option is C $$ 10  \mathrm{cm} $$
We know that on the axis of magnet,
$$\dfrac{B_1}{B_2} = \dfrac{d_1}{d_2} \dfrac{ ({d_2}^2  - l^2)}{( {d_1}^2  - l^2)} $$

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

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

Physics

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