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Re: [Phys-L] Field Lines and charges

On 07/03/2012 09:06 AM, LaMontagne, Bob wrote:
Consider a configuration of two point charges of value +q, one placed
on the x axis of a standard x-y-z coordinate system at +a and the
other at -a. Now look at the electric field vectors - specifically
along the y axis.

OK.

For any position along the positive y axis the field vector points
in the positive y direction. The field magnitude is zero at y = 0,
and as y increases, grows and forms a maximum at y = 0.707 a, and
then gradually goes to zero as y increases further in value.

OK.

One
could trace a field line starting at y=0, x=0 and follow it along the
positive y axis to positive infinity.

No.

. One
could trace a field line starting at y=0, x=0 and follow it along the
negative y axis to negative infinity.

No.

Here is a pair of field lines that do not follow the usual maxim of
starting and stopping on a charge.

The usual maxim is correct. It is not violated in this situation.

At the origin there is no field, and no field lines.

There are field lines in the /neighborhood/ of the origin, but they do not
start at the origin. They swoop in from regions to the left and right of
the x=0 plane. Draw the picture.
http://www.ece.drexel.edu/courses/ece-e304/e3042/conduc4.jpg

I don't recommend drawing any field lines in the plane of symmetry ...
but if you insist on doing so, realize that they represent a set of
measure zero. If they exist at all, they start and end on so-called
charges that have a negligible, infinitesimal amount of charge. Feel
free to add some imaginary charge(s) _of magnitude zero_ at or near
the origin, if you think you need that to explain the field in the
plane of symmetry.