, 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 Eq. (58) and remembering the equalities in Eqs. (57) and (61), we have
or
This shows that the magnitude of the charge transforms in the same way as
lengths and times. 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
. Any proper
or rest quantity, from now on, will be denoted by a zero subscript. 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