, in the
primed frame, is defined as
Copyright © 1999-2000 David E. Rutherford
All Rights Reserved
The charge density,
, in the
primed frame, is defined as
where 
is the magnitude of the charge and
is the
volume containing the charge as measured by an observer at rest in the primed
frame. Using the Jacobian,
, of
, we can
find the magnitude of the charge as measured by an observer at rest in the
unprimed frame. Since we are making an instantaneous measurement of the volume,
we take 
, so that
where
Therefore, the volume in the unprimed frame is
Using (13.4), (14.1), (14.2) and (14.4), we have
or
This shows that the magnitude of the charge transforms in the same way as
lengths. The magnitude of the charge at rest in the primed frame,
, in
this case, is the rest or proper charge. The proper charge will be
referred to, from this point on, as
. We
can now write the relationship between the proper charge,
, and
the improper charge,
, as
Copyright © 1999-2000 David E. Rutherford
All Rights Reserved
E-mail: drutherford@softcom.net