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Re: [Phys-L] Field Lines and charges





________________________________________
From: phys-l-bounces@mail.phys-l.org [phys-l-bounces@mail.phys-l.org] on behalf of John Clement [clement@hal-pc.org]
Sent: Wednesday, July 04, 2012 3:22 PM
To: Phys-L@Phys-L.org
Subject: Re: [Phys-L] Field Lines and charges

It was already mentioned by me, and I pointed out that they were very thin,
in other words not very important. The problem of course is that you have a
singularity at the center. You can define the direction of the field lines
everywhere except at that point. I tend to think geometrically before using
something like Gauss law which of course is valid. I don't like the word
obeyed because it connotes something promulgated to be obeyed, when a law is
merely a relationship which is sometimes or even always valid under
appropriate circumstances.

--------------
[LaMontagne]
Not a singularity in the usual sense. The field very smoothly goes through zero (almost linearly) as you move from the upper y axis to the lower through the origin.
-----------------------

This is similar to the situation where you try to define the rotational
velocity of the center of a solid wheel. It certainly can be defined in the
limit of zero radius. The direction and speed of any particle in the wheel
can be defined at any point, but the direction has no meaning at the center
where there is no speed.

The big problem is if a student notices these lines coming out and not
connected to a charge. For the short answer you can appeal to the lines
coming in perpendicular and say they are connected. The calculus student
might like the idea that this is a singularity where the direction is not
defined. As a vector with zero magnitude has no defined direction, the
arrow becomes a dot.

-----------
[LaMontagne]
That's where this came up. I was preparing fall classes and trying to anticipate student questions based on the reading in the new text we will use. A diagram showed two field lines just above and nearly parallel to the x axis melding into a single line on the y axis. I figured someone might ask since it is emphasized that lines can't cross. I appreciate your insight.
------------


John M. Clement
Houston, TX


On 07/03/2012 09:06 AM, LaMontagne, Bob wrote:
Here is a pair of field lines that do not follow the usual maxim of
starting and stopping on a charge.

I don't buy it, for a reason nobody has mentioned yet: in
addition to the
lines flowing out from the origin in the plane of symmetry,
there are also
lines flowing *into* the origin along the axis of symmetry.

Just because we didn't mention them doesn't mean they are not
there. I'm
kicking myself for not mentioning them earlier. The
inflowing lines have
just as much significance (i.e. not much) as the outflowing
lines. These
lines have virtually no significance because the density of
lines is zero
at the origin.

--------------------------------
[LaMontagne]
Thanks - that appears to be a good resolution of the apparant
paradox. If the density of field lines is zero at the origin,
then the starting and stopping of lines there simply becomes
an ill posed question.

Bob at PC
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_______________________________________________
Forum for Physics Educators
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