Question:
Verify the Ampere’s law for the magnetic field of a point dipole of dipole moment
Take C as the closed curve running clockwise along i) the z-axis from z = a > 0 to z = R; ii) along the quarter circle of radius R and centre at the origin, in the first quadrant of x-z plane; iii) along the x-axis from x = R to x = a and iv) along the quarter circle of radius a and centre at the origin in the first quadrant of the x-z plane.
Solution:
(a)
Along z-axis, magnetic field = μ0M/4π(1/a2-1/R2)
(b)
Magnetic field at point A on the circular arc is = μ0m/4πR2
(c)
The magnetic moment is 0
(d)
The magnetic moment is 0