Hi,

I've got a potentially easy problem with the relativistic
transformations for the electrical fields, perhaps someone can help me
out. I can't figure it out.

Assume you've got an infinite sheet of charge in motion. Then
according to Maxwell's equations, there will be a constant E-field
perpendicular to the sheet, plus a wave starting out from the sheet
the moment it is set in motion with E- and B-fields perpendicular to
the direction of propagation of the field and perpendicular to each
other. That is, there will be a component of the E-field *parallel* to
the plane of the sheet as long as the sheet is in motion.(cf. e.g.
Feynman Lectures Vol. 2 18-4).

If we consider the inertial system where the sheet of charge is at
rest, there will be no current and therefore no B-field. The charge
density changes, but that should have an effect only upon the E-field
perpendicular to the plane. That is, as far as I can see, there should
be no field at all *parallel* to the plane.

But according to the relativistic transformation formulas for the
E-field, the component of the E-field parallel to the motion of the
inertial system in which the field is to be transformed, is unchanged.
That is, it should be zero still in an inertial system moving
relatively to the sheet of charge, i.e. a system where the sheet
moves.

So why is it that according to Maxwell's equations there should be
such a parallel component of the field? Any ideas?