Question

The magnetic field at a point, 10 cm away from a magnetic dipole, is found to be 2.0 $\times {10}^{-4}$T. Find the magnetic moment of the dipole if the point is (a) in end -on position of the dipole and (b) in broadside-on position of the dipole.

Answer 1

Given B = $2\times {10}^{-4}$ T,

d = 10 cm = 0.1 m.

(a) If the point is at end on position.

B = $\frac{{\mu }_0}{4\pi }\frac{2M}{d^3}$

$2\times {10}^{-4}=\frac{{10}^{-7}\times 2M}{({10}^{-1}{)}^3}$

M = $\frac{2\times {10}^{-4}\times {10}^{-3}}{{10}^{-7}\times 2}$

M = 1A- $m^2$.

(b) If the point is at broad side on position

B = $\frac{{\mu }_0}{4\pi }\frac{M}{d^3}$

$\Rightarrow 2\times {10}^{-4}\frac{{10}^{-7}\times M}{({10}^{-1}{)}^3}$

$\Rightarrow M=2A-m^2$