Question

Let r be the distance of a point on the axis of a magnetic dipole from its centre. The magnetic field at such a point is proportional to

(a) $\frac{1}{r}$
(b) $\frac{1}{r^2}$
(c) $\frac{1}{r^3}$
(d) none of these

Answer 1

(c) $\frac{1}{r^3}$

Magnetic field B due to a bar magnet of magnetic moment M at distance r of the point on the axis from its centre is given by
$B=\frac{{\mu }_{\mathit{0}}2Mr}{4\mathrm{\pi }{\left(r^2-l^2\right)}^2}$

Here, 2l is the length of the magnet.
When the distance of the point where the magnetic field has to be calculated is greater than the length of the magnet, i.e $r>>l$, the bar magnet acts like a magnetic dipole whose magnetic field is
B$\propto \frac{1}{r^3}$
Now, l in the denominator can be neglected.
So, the correct option is (c).