I'm a big believer in the pedagogical rule that says to
start with the right answer. At some later stage there
will be time to deal with whatever misconceptions might
remain.
So, let's consider coupling to an electroscope by induction.
1) Start with just the electroscope by itself. Discharge
it. This creates a zero-voltage, zero-charge situation.
The leaves are not deflected.
2) Now bring up a positively-charged object, so that it is
near but not touching the terminal. This induces a dipole
distribution of charge on the guts of the electroscope:
negative charge on the terminal, and positive charge on
the leaves. The total charge on the guts remains zero.
The guts are at some nonzero voltage. The leaves are
deflected. This is called induction.
3) Now ground the terminal by touching it briefly with your
finger. This brings the guts to zero voltage. The total
charge on the guts is strongly negative. The charge is
concentrated on the terminal. There is virtually zero
charge density on the leaves. The leaves are not deflected.
In this situation, we have a crude, ill-characterized
capacitor. There is a mutual capacitance between the
object and the terminal.
4) Now move the object away. The capacitance goes down.
The charge stays the same. This means there must be
an increase in the voltage, i.e. the voltage across
the gap between the object and the terminal. The
voltage on the guts goes from zero to some strongly
negative voltage. Also the charge on the guts gets
redistributed. A goodly amount of the charge that was
confined to the terminal moves onto the leaves. The
leaves are deflected.
Terminology: I use the term /guts/ to refer to the
/terminal/ and the /leaves/ and whatever connects them.
The guts are insulated from the /case/. I assume the
case is grounded
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To avoid misconceptions:: In step (2) above, please do
*not* refer to this as "charging" by induction. Call
it /coupling/ to the electroscope by induction. You
could also call it /polarizing/ the electroscope by
induction. There was zero charge on the guts in
step (1), and there remains zero charge in step (2).
On the other side of the same coin: In step (3), please
do *not* refer to this as "discharging" the electroscope.
Call it grounding if you wish. You are zeroing the voltage,
not zeroing the charge.
Thirdly: Do not talk about "the" charge on "the" electroscope,
especially when there is coupling by induction. There is not
necessarily any simple relationship between the charge on the
terminal and the charge on the leaves. The terminal and the
leaves have the same voltage, but not generally the same charge
or the same charge density.
More generally, be fastidious about the distinction between
charge and voltage. Blurring this distinction makes as much
sense as blurring the distinction between distance and force
... i.e. no sense at all.
Recently I was dealing with a situation where there were
about five misconceptions layered on top of each other.
This is a pedagogical nightmare. We are supposed to teach
things one at a time, so that each new success builds on
previous successes. But when there are N misconceptions
stacked on top of each other, even after you have dealt
with N-1 of them you're still getting the wrong answer,
so it doesn't look like progress.
I was wondering where all these misconceptions could be
coming from ... so I looked at some youtube videos. The
first one I came across was from Carleton University, which
I have always considered a reputable place. http://www.youtube.com/watch?v=cMM6hZiWnig
Basically everything the guy says about charge is wrong.
Among other things, he tramples the distinction between
charge and voltage.
Also he talks about "the" charge on "the" electroscope,
which is nonsense, especially in the case of coupling
by induction, as discussed above.
I reckon that part of the problem is that people cannot
directly /see/ the charge. They guess what the charge is
doing, and they often guess wrong.
If you want another example of a physics professor getting
this wrong, consider the book _Matter and Interactions_
which claims to be a modern textbook based on enlightened
pedagogical principles. The diagrams systematically equate
charge density with voltage. There are about a dozen
disclaimers saying the diagrams are only "rough approximations"
... but even that's not true. It's not even an acceptable
approximation in many cases. This is terrible pedagogy,
because it guarantees that students will get the wrong
impression.
I realize that estimating the voltage is easy and estimating
the charge density is hard. In the real world, when people
want to predict the charge distribution, they use a computer,
using iterative numerical methods. The geometry of an electro-
scope is simple enough that you can more-or-less figure out
the charge distribution by hand, but it takes some effort.
In any case, there is no excuse for teaching wrong stuff just
because it is easy.
So: We have identified some misconceptions. They are
widespread ... but they remain misconceptions nonetheless.
Please don't require students to learn wrong stuff. This is
the opposite and the enemy of critical thinking.