Narrow Results

It is generally assumed in the literature that a Lorentz transformation on a neutral current loop results in a moving current loop with a nonvanishing charge distribution and an electric dipole moment. We show in this paper that this is not, in fact, correct. The derivation that leads to the charge distribution was based on an incomplete Lorentz transformation, which transforms the charge-current four-vector $j^{\mu }=[\rho (r,t),j(r,t)]$, but not the space–time four-vector $x^{\mu }=(t,r)$. We show that completing the Lorentz transformation by using the variable $t^{\prime }$ in the moving frame, rather than keeping the rest frame time variable $t$, results in there being no induced charge density and no resulting electric dipole moment.

The dipole–dipole interactions may lead to the linear chain formation in the ferrofluids. When the dipolar interaction energy is much larger than the thermal energy, the average length of the chains 〈n〉 becomes much larger than 1. This strongly influences on the magnetic susceptibility χ which is enhanced in comparison to its Langevin value χ_L by a factor of 2〈n〉.