Question

The magnetic induction in air at a distance d from an isolated point pole of strength $m$ unit will be
A. $\dfrac{m}{d}$
B. $\dfrac{m}{{{d}^{2}}}$
C. $md$
D. $md^2$

Answer 1

Hint: In this question we will use the concept magnetic induction of a bar magnet to get the magnetic induction in at a distance d from an isolated point pole of strength m unit.

Complete step by step solution:
In a bar magnet with N=north pole, S=south pole and O=centre. If a point is perpendicular to the bar magnet, in line with O, then that is the broad-side-on position for magnetic induction. If a point is on the extended axis of the bar magnet, in line with N and S, then that is the end-on position for magnetic induction.

For a single point having strength m, all the positions are end-on. At end-on position,
$B=K\times \dfrac{m}{{{r}^{2}}}$
where, K=constant, B=magnetic induction, m = pole strength and r=distance
Therefore, the magnetic induction in air at a distance d from an isolated point pole of strength m unit will be $\dfrac{m}{{{d}^{2}}}$.

Hence, the correct answer is B.

Additional Information: Magnetic induction is the process through which a regular piece of iron briefly gains magnetic properties as a result of the presence of another magnet nearby. A current is created by voltage production (also known as electromotive force) as a result of a shifting magnetic field. This can occur when a conductor is put in a magnetic field that is moving (when utilising an AC power source) or when a conductor is continuously moving in a magnetic field that is stationary.

Note: For a single point, there can never be a broad-side-on position since there is no perpendicular of a point. All the points at a distance of the point with strength m will always be an end-on position because we can assume that the point taken is on the x/y/z axis.