Question

Assertion: Magnetic force between two short magnets, when they are co-axial follows inverse square law of distance
Reason: The magnetic forces between two poles do not follow inverse square law of distance.
 $ \left( A \right) $ Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
 $ \left( B \right) $ Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
 $ \left( C \right) $ Assertion is correct but reason is incorrect.
 $ \left( D \right) $ Both assertion and reason are incorrect.

Answer 1

Hint: Since we know that the magnetic force between two short magnets when they are co-axial is given by $ \dfrac{{{B^2}}}{{2{\mu _ \circ }}}A $ , and the magnetic force between the two poles is given by $ \dfrac{{\mu {q_1}{q_2}}}{{4\pi {r^2}}} $ . So by observing these two formulas we will be able to answer this question.

Formula used:
The magnetic force between two short magnets when they are co-axial, $ \dfrac{{{B^2}}}{{2{\mu _ \circ }}}A $
Here, $ B $ , will be the magnetic induction which will be for a very short duration.
 $ A $ , will be the contact surface area between two nearly touching magnets
 $ {\mu _ \circ } $ , will be the permeability of free space
The magnetic force between the two poles, $ \dfrac{{{\mu _ \circ }{q_1}{q_2}}}{{4\pi {r^2}}} $
Here, $ {q_1}\& {q_2} $ is the charge.

Complete step by step answer
As we know from the hint that the force between two short magnets when they are co-axial, $ \dfrac{{{B^2}}}{{2{\mu _ \circ }}}A $ and the magnetic force between the two poles, $ \dfrac{{{\mu _ \circ }{q_1}{q_2}}}{{4\pi {r^2}}} $ .
And the inverse square law is given by $ X \prec \dfrac{1}{{{d^2}}} $ . So from the above two expressions, we can see that the above expression is not following the inverse square law of distance. And hence, from this, we can say that both the assertion and reason is incorrect.
Therefore, the option $ \left( D \right) $ is the correct answer.

Note:
Inverse square law of distance followed by the gravitational forces and the electromagnetic forces. In this, there will be a variation of the physical quantity which will be done with respect to the distance. As the distance between the objects increases the intensity will get decreased.