### Re: Does charge flow from high to low potential?

Date: Sun Jul 5 19:50:45 1998
Posted By: Bernard Gilroy, Secondary School Teacher, Science (Physics, Astrophysics), Holy Ghost Preparatory School
Area of science: Physics
ID: 892921446.Ph
Message:

This depends on the sign of the charge.  Positive charge flows from high to
low electric potential.  Negative charge, alas, flows from _low_ potential
to high potential.

This apparent inconsistency comes from the actual fact, which is that
particles tend to move toward a situation of minimized _potential energy_.
That is, a charge q will move from point A to point B if U(B) < U(A).
(Note that this is necessary.  For a charge to spontaneously move from A to
B would require its kinetic energy to be negative ... not possible.)

Here's the confusion: The potential energy of a charge q in a potential V
is given by U = q V.  If q>0, everything's peachy: this forces V(B) < V(A)
as hoped for.  But say q < 0.  In fact, assume q = -q0 (where q0>0).  This
allows us to treat the negative sign explicitly.  In this case, since U = q
V, we have
-q0 V(B) < -q0 V(A).  Since q0 > 0, we can divide without changing
sense, so
-V(B) < -V(A).  Now we divide by -1 _and flip the sense_:
V(B) > V(A).

So the negative charge moves from low potential V(A) to a higher potential
V(B).  Ta-da!

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