Question

If the distance between two similar poles of
equal strength is doubled, to get the same repulsive
force, the pole strength of each pole should be
(A) increased by 2 times
(B) increased by 4 times
(C) halved
(D) doubled.​

Answer 1

refers to the attachment above

Answer 2

Answer:

If the distance between two similar poles of equal strength is doubled, to get the same repulsive force, the pole strength of each pole should be (D) doubled.​

Explanation:

Let m1 and m2 be the pole strength of each pole, d be the distance between the two poles, and F be the repulsive force.

The force between two magnetic poles is directly proportional to the product of their strengths and is inversely proportional to the square of the distance between them.

Therefore, the repulsive force is given as

$F=\frac{m1 *m2}{d^2}$

It is given that the distance between the poles is doubled. Therefore,

$F=\frac{m1*m2}{(2d)^2}$

$F=\frac{m1*m2}{4d^2}$

Doubling the distance between the poles decreases the force of repulsion by a factor of 4. Hence, to get the same repulsive force, we increase the pole strength too.

$F=\frac{4m1*m2}{4d^2}$

Since the poles have equal strength,

$F=\frac{(2*m1)(2*m2)}{4d^2}$

Therefore, the pole strength of each pole must be doubled.

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