  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 $j^\mu=[\rho({\bf r},t),{\bf
j(r},t)]$, but not the space-time four-vector $x^\mu=(t,{\bf r})$.
  We show that completing the Lorentz transformation by using the variable $t'$
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.
