  In the 1960s, E.M. Purcell presented a basic explanation of the magnetic
force experienced by a test charge moving parallel to a stationary
current-carrying wire. According to Purcell's derivation, this force results
from the difference between the relativistic length contraction of the distance
among the stationary positive charges of the wire and the relativistic length
contraction of the distance among the negative charges moving in the wire when
the charges are observed in the rest frame of the test charge. The contraction
difference generates a charge density imbalance that, in the rest frame of the
test charge, is experienced as an electrostatic force, while, in the lab frame,
is perceived as the magnetic force. In the present paper, we show that
Purcell's approach is problematic since it generates inconsistencies and
paradoxes. We maintain that Purcell's derivation has only an illustrative and
expository value and should not be taken literally as describing something that
really and physically happens in the wire. Furthermore, we believe that the
difficulties pointed out here should be explicitly presented and discussed when
introducing Purcell's approach in physics courses at the undergraduate and
graduate levels.
