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Re: long-range fields, was: ice-pail experiment



At 03:26 PM 3/25/00 +0200, Savinainen Antti wrote:
My students asked:

Why the positive charge is totally on the outer surface after the metal
ball has touched the inner surface (the ball and the inner surface will be
neutral)? Wouldn't it make more space for the charges that repel each
other if they were distributed both to the inner and the outer surface?

The short answer is: Electrostatics is a _long range_ field. By moving
from the outside surface of the pail to the inside surface, some of the
charges could move away from their nearby neighbors, but they would be
getting closer to whole lot of far-away neighbors on the far side of the pail.

The students are suffering from a quite understandable misconception about
the meaning of "nearness" and "room" and "neighbor". In everyday
experience, if we try to pack N students into an elevator, their perception
of how much "room" they have depends on their distance to their closest
neighbor; the distance to far-away neighbors is irrelevant to the
perception of roominess.

But the electrostatic square-law force means that a steradian of charged
surface far away is EXACTLY as repulsive as a steradian of charged surface
nearby (assuming they have the same charge per unit area).

The picture is hard to draw in ASCII art; you have to imagine that the
angles below are SOLID angles subtending an area not an arc. We have 32
charges at a distance of 4 on the left, 8 charges at a distance of 2 on the
right, same charge per unit area, and equal-and-opposite forces on the test
charge in the middle.

++++\
++++ \
++++ \ /++
++++ \_/ ++
++++ / \ ++
++++ / \++
++++ /
++++/

Build a model if you must, to portray the actual 3-D situation for your
students.