Question

The magnetic field at a point, 10 cm away from a magnetic dipole, is found to be `2.0 xx 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:
Magnetic field strength, B = `2 xx 10^-4  "T"`

Distance of the point from the dipole, d = 10 cm = 0.1 m

(a) If the point is at the end-on position:
The magnetic field (B) on the axial point of the dipole is given by B = `u_0/(4pi) (2M)/d^3`

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

`therefore` `2 xx 10^-4 = (10^-7 xx 2M)/(10^-1)^3`

⇒ `M = (2 xx 10^-4 xx 10^-3)/(10^-7 xx 2)`

⇒ `M = 1 A -  "m"^2`

(b) If the point is at broadside-on position (equatorial position):
The magnetic field (B) is given by 

B = `u_0/(4pi) M/d^3`

⇒ `2 xx 10^-4 = (10^-7 xx M)/(10^-1)^3`

⇒ `M = 2A - "m"^2`