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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.
Solution
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`
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