Question

The magnetic field at a point, 10 cm away from a magnetic dipole, is found to be 2.0 × 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

(a) The magnetic moment of the dipole if the point is in end-on position of the dipole is $1 A-m^{2}$

(b) The magnetic moment of the dipole if the point is in broadside-on position of the dipole is $2 A-m^{2}$

Explanation:

Strength of Magnetic field, B = 2 × 〖10〗^(-4) T

Point distance from dipole, d = 10 cm = 0.1 m

(a) If the end-on position is set to the point:

The magnetic field The dipole's axial point is given by

$B=\frac{\mu_{0}}{4 \pi} \frac{2 M}{d^{3}}$

Here, M is the magnetic moment we need to find out about the dipole.

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

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

         $M=1 A-m^{2}$

(b) If the place of the point is broadside-on (equatorial position):

The magnetic field B is given by

         $B=\frac{\mu_{0}}{4 \pi} \frac{2 M}{d^{3}}$

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

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

         $M=2 A-m^{2}$