Reply: Voltage and Van de Graaff

[Larry Brown]

Bob,

After reading the explanation so ably written by Don Simanek, I'm tempted to
keep silent, but...

I agree completely with Don. The Mechanical Universe (High School
Adaptation) gives these analogies: the electric field is like the
gravitational force on, say, a ball on a hill side; it is down the slope in
the direction of maximum value; the electric potential is the height above
some point (sea level, the bottom of the hill, etc). It is as if you climb a
hill (increasing the voltage, doing work against the field) and reach a
plateau, or a lake, which will be flat, no gravitational force in the
direction of motion, and therefore representing constant potential. SO,
outside the Van de Graaff, the voltage is going (actually negative, since it
is being charged with electrons) up as points closer and closer to the dome
are considered. But once inside the dome, the voltage is relatively constant
(high value, but constant), and the field is essentially zero, within
conditions mentioned by Don in his last paragraph.

Fun stuff. It sure "turns on" the kids.

Larry

[Pat Callahan pxc17@psuvm.psu.edu]

The original post concerning this question asked about the "voltage"
inside the sphere. I belive a problem may exist in the question since
the author was using a term (voltage) that could apply to a) Electric
Potential or b) Electric Potential Difference. The answer would depend
upon which of the two values you are asking about. When I teach
electricity to my students I try to urge them to use correct terminology
and encourage them to avoid using the unit as the name for the quantity.
We don't use "amperage" in place of current, nor do we use "voltage"
when we are discussing potential difference. Unfortunately it is common
practice in the technical field to use the unit in place of the name for
the quantity.
Pat Callahan

[Donald E. Simanek]

Pat, I fully agree, and this voltage, amperage, wattage stuff has been
one of my pet peeves for many years. Now try to get the textbook authors
to see the light and clean up their language. :-)

We don't use 'meterage' for length, 'gramage' for weight or 'hertzage'
for frequency, do we?

And we say we are measuring the voltage when in fact we may be measuring
millivoltage. Why not say 'millivoltage' then?

And then there's 'percentage', used far too often, in cases where
'percent' would be quite sufficient.

Some folks think that adding '-age' to something makes it sound more
profound.

However, in the original query about potential within the metal sphere,
the missing ingredient was a specification of 'potential with respect to
what?' This falls into a different category of verbal trap. We can ask
"What is the field inside" with no ambiguity. But with potential we
must specify a reference potential.

With inverse square fields, such as those from point charges, and even
with fields from finite distributions of charge within a finite volume,
one can specify the potential at infinity as reference value zero, and we
usually do so, sometimes without bothering to state that fact. If we speak
simply of 'the potential at point x' one assumes, by default, that we are
taking the potential at infinity to be zero. But with fields from infinite
charges, or distributions which extend to infinity (as the classic
'infinitely long, straight wire') one cannot have zero potential at
infinity. [I don't know a non-calculus way to prove that; sorry.]

Anyway, the bottom line on the static charge on a conductor is that the
field inside is zero and the potential throughout is the same as that on
the surface. In the non-static Van de Graaff, the field inside the dome is
nearly zero (certainly small compared to the field *outside*), and the
potential inside doesn't vary much compared to the potential of the
surface (referenced to infinity).

-- Donald