Hello
I have a question about electromagnetic field transformation between
different inertial frames.
Consider the following case:
A charge q1 is kept stationary with respect to another charge q2 which
is moving with velocity v. When the moving charge is in a position such
that the line connecting it with the other charge is normal to the
direction of motion, Coulomb's law says that the field in the 2 frames
=q1 q2/4pi.epsilon.r^2. This expression has the same value in both
frames since all the quantities in it are invariant. (r is normal to
the velocity) While Lorentz transformation of the electric field says
that the field will differ by a factor of gamma (Here the electric
field has one component : in the direction normal to velocity)

We can imagine further that there is a shield between the 2 charges
having a hole just in the line connecting them in this position to
eliminate the field at other positions of the moving charge and hence
time retardation effects.
Thanks.

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