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[Phys-L] Re: Electric Field



You have a field plotting apparatus? This has been discussed previously.

At a more advanced level (algebra), Harnwell discusses this exact
problem (W/O bivectors, of course). Plotting the equipotentials and
then drawing normals * is much easier than most other methods.

* for those who can't differentiate.

bc

p.s. discusses at the same place the two equal (and unequal in
magnitude) charges.

David Abineri wrote:

John, Thanks for this response, and to your many responses over the
years to this list. It does, however, beg two questions in my mind:

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.

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)?

Thanks again, David Abineri




In looking at the electric field about a pair of equal but opposite
fixed point charges situated on the x axis in my high school class, we
mapped part of the field by looking at the forces exerted on a test
charge (proton) by the two fixed charges. A student then asked me to
show that if one places the test charge to the left of the left-most
charge (the positive charge) but just slightly above the x axis that the
field line that it would follow would in fact 'circle' around in a large
path until it eventually approaches the other charge from the upper
right. It seems to me that the force of repulsion would always tend to
push the charge leftward making it difficult to see how it would ever
'circle' to the right.

Is there a way to see that the test proton will eventually move
rightward? Any help appreciated. Thanks.




It won't. Your intuition is correct. The field line that passes
through the test charge's initial position clearly does wrap around
to the right and eventually approaches the negative charge from the
upper right. But the test charge doesn't follow that field line or
any other field line. Instead it receives a relatively big initial
push to the left and slightly upward that gives it a relatively large
amount of momentum in that direction. After a short time it finds
itself in a region where no significant force acts on it and it
coasts to the left and slightly upward forever.

Exploring the behavior of a charge released from rest in an
electrostatic field is a good way to develop one's appreciation of
inertia and also of the difference between velocity and acceleration.

A positive charge released from rest always STARTS moving in the
direction of the field line, but if the field line curves, the charge
CAN'T follow it because of its inertia. It is the acceleration that
is always in the direction of the field, NOT the velocity.

All of that said, it is interesting to note that in a world dominated
by viscosity, Newton's Second Law essentially becomes

sum of all forces EXCEPT viscosity
velocity = -----------------------------------
viscous drag coefficient

In such a world, objects subject only to the electric force DO follow
electric field lines.

--
John "Slo" Mallinckrodt

--
dabineri@fuse.net




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