A stationary magnetic dipole, is situated above an infinite uniform surface current, (...

A stationary magnetic dipole, is situated above an infinite uniform surface current, (Fig. 12.44).

(a) Find the torque on the dipole, using Eq. 6.1.

(b) Suppose that the surface current consists of a uniform surface charge σ, moving at velocity so that K = σv, and the magnetic dipole consists of a uniform line charge λ, circulating at speed v (same v) around a square loop of side l, as shown, so that m = λvl². Examine the same configuration from the point of view of system moving in the x direction at speed v. In the surface charge is at rest, so it generates no magnetic field. Show that in this frame the current loop carries an electric dipole moment, and calculate the resulting torque, using Eq. 4.4.

Equation 12.44

Reference Equation 6.1

Reference Equation 4.4