[Phys-L] Re: Electric Field

[John Mallinckrodt <ajm@CSUPOMONA.EDU>]

David writes:

> 1.  Is there a better way to introduce the notion of Electric Field
> to beginning students?  I understand that the inertia of the test
> charge means that it will only start along a field line and  not
> stay on it but it sure is an appealing approach since they, at this
> stage, understand forces fairly well.

Inertia should play no role in explaining the concept of the electric
field.  Talking about the motion of charges in an electric field is
conceivably the worst way to introduce students to the concept.  It
muddies the water by needlessly convolving two difficult ideas.

I see no fundamental problem with the standard approach involving an
operational definition of the electric field, which is, briefly:

Select a positive charge small enough so as not to disturb the
distribution of other nearby charges (or simply imagine for the sake
of this procedure that it DOESN'T disturb that distribution!), place
it at a position of interest, calculate all the electric forces on
it, and divide that force by the charge itself.  Notice that the
result depends ONLY on the position of interest and NOT on any
property of the charge that was used to determine it.  Use that fact
to appreciate the concept of a "vector field" (a vector quantity that
has a definite value at every position on space) and to see that it
is not so different from the concept of a "scalar field" like the
daily high temperatures on a weather map.

"Lines" are determined very simply by following the procedure above,
moving to a new point of interest a very short distance away in (or
opposite) the direction of the electric field, and repeating as
necessary.

As always, it doesn't begin to be enough simply to say all of this.
Students have to put a pencil in their hands and REALLY follow the
procedure somewhat rigorously for two or three examples of
progressively greater difficulty.

Now, at some point later on I like to spend a little time exploring
what happens when you release a charged object in an electric field
to make sure that students also understand that charges DO NOT follow
electric field lines.

>  2.  May I ask the question again, postulating a massless
> (inertia-less) test charge?  Or, how does one show that the filed
> line does come all the way around (at the elementary level of
> course)?

Newtonian mechanics is more than a little ambiguous about what
happens when you exert a force on a massless particle so I wouldn't
go there in the context of this topic.  If you must (and I would
argue against it) it would be better to consider the motion of a
charged particle in a tremendously viscous and stationary fluid. This
prevents the particle from ever developing a nonnegligible momentum
which effectively removes the influence of its inertia on its motion.

Regarding the field line "coming around":  Following the procedure
discussed above for a dipole ought to be enough to convince most
students of the plausibility of the result.  IMO, the best way is to
start at a point far away on the perpendicular bisector and extend
the line forward and backward from there.  It's easy to see what
happens to such a line and to imagine what must happen for lines
through points even FARTHER away on the perpendicular bisector.

--
John "Slo" Mallinckrodt

Professor of Physics, Cal Poly Pomona
<http://www.csupomona.edu/~ajm>

and

Lead Guitarist, Out-Laws of Physics
<http://www.csupomona.edu/~hsleff/OoPs.html>
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