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) 1r
(b) 1r2
(c) 1r3
(d) none of these

Answer 1

Let r be the distance of a point on the axis of a magnetic dipole from its centre. The correct option is (d - none of these).

1) We have, magnetic field B for a bar magnet of Magnetic moment at a distance r from a point on the axis of a magnetic dipole from its centre is given by,

B = (u/4 * Pi) * ( 2 Mr / (r^2 - l^2)^2)

2) From the above equation, it can be seen B is proportional to r / (r^2 - l^2)^2

Answer 2

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 $\frac{1}{r3}$

Explanation:

Step 1:

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

$B=\frac{\mu_{0}}{4 \pi} \frac{2 M r}{\left(r^{2}-l^{2}\right)^{2}}$

Here, the length of the magnet is 2l.

Step 2:

When the distance from the point at which the magnetic field is to be measured is larger than the magnet length, i.e.  

r >>l,

Step 3:

The magnet bar acts as a magnetic dipole with a  $B \propto \frac{1}{r^{3}}$  magnetic field

Then, one can ignore l in denominator.

Therefore the correct answer is Option(c)