Re: [Phys-L] Field Lines and charges

["LaMontagne, Bob" <RLAMONT@providence.edu>]

> -----Original Message-----
> From: phys-l-bounces@mail.phys-l.org [mailto:phys-l-bounces@mail.phys-
> l.org] On Behalf Of John Denker
> Sent: Tuesday, July 03, 2012 12:46 PM
> To: Phys-L@Phys-L.org
> Subject: 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

[] 

[LaMontagne, Bob] 

I agree with the two "no" comments above on the basis of the technicality that the field is zero at the origin. However, along the y axis, at say, 0.7 a, there is definitely a field - and it can be traced in a continuous manner up the y axis - hence a field line. If one is going to argue that there is no field line if the field is zero, then you cannot follow that particular line back to the two charges - there is no "swoop" for this particular case of being right on the axis.


> 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.
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