Question

The field due to a magnet at a distance R from the centre of the magnet is proportional to
(A) ${R^2}$
(B) ${R^3}$
(C) $\dfrac{1}{{{R^2}}}$
(D) $\dfrac{1}{{{R^3}}}$

Answer 1

Hint:
In order to solve this question, we will first write down the formula of the magnetic field due to a bar magnet at some point on its axis and then we will determine the relationship between the magnetic field and distance and will check for the correct option.


Complete step by step solution:
As we know that, the magnetic field due to a bar magnet having magnetic moment M at a distance of R from its centre on its axis is calculated using the formula $B = \dfrac{{{\mu _o}}}{{4\pi }}\dfrac{{2M}}{{{R^3}}}$ where, ${\mu _o}$ is known as the relative permeability of free space so, we see that magnetic field due to a bar magnetic B on its axis at a point of distance R is related as $B \propto \dfrac{1}{{{R^3}}}$ , also let us check magnetic field due to bar magnet at a distance of R on the equatorial point and it’s given by $B = \dfrac{{{\mu _o}}}{{4\pi }}\dfrac{M}{{{R^3}}}$ here also we see that, $B \propto \dfrac{1}{{{R^3}}}$ so we see that magnetic field is always inversely proportional to cube of distance R irrespective of point we choose either the point on axis or the point on equatorial line.
Hence, the correct answer is option (D) $\dfrac{1}{{{R^3}}}$



Therefore, the correct option is D.




Note:
It should also be noted that the magnetic field due to a bar magnet on its axis point is always twice the value of the magnetic field on its equatorial point while keeping the distance the same from the center of the bar magnet in both cases.