[Phys-L] Re: Elecric Field Lines

[John Mallinckrodt <ajm@CSUPOMONA.EDU>]

> > So the somewhat surprising fact is that NO field line approaches
> > the y-axis for very long.
>
> Actually, that didn't seem at all surprising to me.  I thought about the
> field far from the charges, which ought to look a LOT like a single
> point charge of 2Q at the origin.  Since that field is spreading
> radially, then any E field lines leaving the charges must eventually
> bend around to head out mostly radially from the origin - i.e. away from
> the y axis.
>
> Shows the power of thinking about the limiting case!

I'm not so sure.  Yes, it does apparently suggest what turns out to
be the right answer, but lots of inadequate ways and even a fair
number of wrong ways of looking at things also give right answers,
especially when there are only two possible answers.

Just yesterday I had every student in a junior E and M class tell me
that, if Cvector dot Avector = Cvector dot Bvector for any Cvector
then we can cancel the Cvector on both sides of the equation and
determine that Avector = Bvector.  That is the right answer, and the
argument is appealing, but it is, nevertheless, wrong.

As you say, "any E field lines leaving the charges must eventually
bend around to head out mostly radially from the origin" but there is
still a fair amount of wiggle room within that ambiguous phrase
"mostly radially from the origin."

The argument CAN be made rigorous by more carefully examining the
cross sections of bundles of field lines (how's THAT for reifying the
concept!) and using the fact that the field magnitude must eventually
decrease as 1/r^2.

Nevertheless, even after making such a rigorous argument I would
STILL reiterate my opinion that it IS somewhat surprising that NO
field line approaches the y-axis after traveling such a short
distance away from the two charges.

--
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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