Question

1. Looking at the force on a magnetic dipoles, there are two models which yield slightly different results a. The force on an electric dipole is F (p. V)Ë because it's made Z of two electric monopole charges. If magnetic dipoles were actually made of Magnetic monopoles (like in the Gilbert model) we would expect F (m V)B, which doesn't experimentally seem to match observations, but derive this equation from the Taylor series: у B(F)B(F)[- ") VB(") d Assume that a magnetic monopole would feel a force: т

Answer 1

Consider such a magnetic dipole system with the coordinate axes so arranged such that the origin lies in the center of the dipole distribution.

The magnetic force density for a magnetic charge density
(72)
is
Η = ηΒ
(which is given in the assumption).

The force on a static distribution of magnetic charge $\eta(r)$ then is:

F = n(r)B(r) dr

Expanding about the center of the charge distribution taken as :

O = D = 1

F= n(r)[B(a) +r. V,B(a) +...]a=o dr

The integral of the first term on the right hand side corresponds to the total magnetic charge of the distribution. We assume that the total magnetic charge of the distribution vanishes so that:

n(r) d’r = 0

The integral of the second term involves the magnetic dipole moment:

m= | rn(r) dr

Neglecting higher order terms, we have:

F = (m.)B