Question

A very small magnet is placed in the magnetic meridian with its south pole pointing north. The null point is obtained $20cm$ away from the center of the magnet. If the earth's magnetic field (horizontal component) at this point be $0.3Gauss$, the magnetic moment of the magnet is

• A. $3.6\times {10}^{3}e.m.u$
• B. $1.2\times {10}^{3}e.m.u$
• C. $2.4\times {10}^{3}e.m.u$
• D. $8.0\times {10}^{2}e.m.u$

Answer 1

The correct option is B $1.2\times {10}^{3}e.m.u$

IMAGE

From the diagram it is clear that , the null point (zero magnetic field) will lie on the axis of the bar magnet at some point A where the magnetic field of bar magnet cancels the horizontal component of earth’s field .

We know that, in CGS system, magnetic field on axis of a bar magnet.

$\left|B\right|=\frac{2M}{r^3}$

Where, $M$= magnetic moment
$r$= distance of point from the centre
at null point $A,r=20cm$

$\therefore \frac{2M}{(20cm{)}^3}=0.3Gauss$

(magnets field will be equal and opposite to earth's horizontal component of field)

$\Rightarrow M=1.2\times {10}^{3}e.m.u$

Thus, magnetic moment of the magnet is $1.2\times {10}^{3}e.m.u$

Hence, correct option is $\left(b\right)$.