Horace wrote:
<snip>
Suppose the DC power supply, a battery, carries a coulomb of excess
positive charge, or a coulomb of excess negative charge?
Charge can always be detected by the field that is around it - provided
you can get "around" it to measure! Gauss's law (I think it is) says
that if you construct a closed surface and then measure the electric
field all over that surface, then the sum (integral) of that measurement
tells you how much charge is enclosed within that surface (fields are
always measurable without needing to connect a meter between two points
- eg by a field-mill).
However if you can't get all around it, and the charge is arranged so
that the field in the areas where you can measure cancels to some
extent, then it is not (currently) possible to know that that charge is
present nearby. This is the situation within a charged sphere (or
Faraday cage) for instance. While ever you are confined to the cage,
you cannot tell from measurements that you can make within the cage
whether you and the cage are charged to a high or low potential.
This is the manner in which potential is unmeasurable - you could be
surrounded by a layer of charge and at a very high potential, but from
within the canceling distribution that the charge occupies on the
external surface of the cage, you cannot measure what the potential (or
phi) is within the cage.
A similar case is true with gravity - you can't in principle tell
whether you are floating near to a lot of mass, or in empty space. If
you can make observations outside your enclosure - such as looking at
spectral lines from distant disturbances, and compare them to the
spectral lines from similar disturbances you can create. Then it
becomes possible to know the difference in gravitational potential
between where you are and the distant observation - as time ticks at a
different rate dependent on your gravitational potential and the
spectral lines will be shifted accordingly.
So it is very likely that there is a similar test that could be done to
measure your electric potential - but in some way you will have sampled
the space outside of your cage by means of the signal that has traveled
from the remote location - through the space with the field in it - to
where you are.
