Question

Let r be the distance of a point on the axis of a bar magnet 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

(d) None of these

Magnetic field B due to a bar magnet of magnetic moment M at distance r of the point on the axis of the magnet from its centre is given by

$B=\frac{{\mu }_o}{4\pi }\frac{2Mr}{{\left(r^2-l^2\right)}^2}$
Here, 2l is the length of the magnet.
So, from the above formula, it can be easily seen that $B\propto \frac{r}{{\left(r^2-l^2\right)}^2}$.