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Re: Potential of a point charge



In my opinion it is desirable to start
(in an introductory course) with a
uniform electric field and generalize
later, not the other way around.

Another desirable think is to make
sure that students are aware that
electric field lines show the downhill
direction for positive q and uphill
directions for negative q. Downhill
means that electric potential energy
is decreasing (negative delta_U).
Once they accept this they are less
likely to be confused by the definition:

delta(U) == -q0 * sum of dot products
of E and ds.

Each dot product is positive on a
downhill segment and negative on an
uphill segment (positive or negative
cosine). That is why we need the minus
sign in the definition of delta U. Without
it delta U would not be negative in
downhill segments, as we want it to be.
Ludwik Kowalski



On Thursday, February 26, 2004, at 04:02 PM, RAUBER, JOEL wrote:

John M.

You forgot the QED at the end.

:-)

Joel R

| -----Original Message-----
| From: Forum for Physics Educators [mailto:PHYS-L@lists.nau.edu] On
Behalf
| Of John Mallinckrodt
| Sent: Thursday, February 26, 2004 1:20 PM
| To: PHYS-L@lists.nau.edu
| Subject: Re: Potential of a point charge
|
| I think this confusion is widespread, but I find that it pretty much
| evaporates if one keeps in mind two things:
|
| 1) The integral involves a dot product of the VECTOR E_vec with the
| VECTOR ds_vec.
|
| 2) When integrating "radially" the vector ds simply becomes the
| vector (dr r_hat) where r_hat is a unit vector in the positive r
| direction (i.e., radially outward) and dr is a SCALAR with an
| algebraic sign that is determined AUTOMATICALLY by the limits of the
| integral. If the lower limit is larger than the upper limit, than dr
| IS negative. One need not "make adjustments" for this fact by
| putting in a minus sign somewhere; its all "in there" already.
|
|
| Thus, to find the absolute potential at a distance R from a point
| charge, we simply apply the definition
|
| delta V = V_B - V_A = - int( E_vec dot ds_vec from A to B)
|
| to a radial path from "infinity" (where V = V_A = 0) to R where (V =
V_B)
|
| V = - int( [k q r_hat/r^2] dot [dr r_hat] from infinity to R)
|
| = - k q int( [dr/r^2] [r_hat dot r_hat] from infinity to R)
|
| = - k q int( dr/r^2 from infinity to R)
|
| = - k q (-1/r evaluated from infinity to R)
|
| = k q/r
|
| --
| John Mallinckrodt mailto:ajm@csupomona.edu
| Cal Poly Pomona http://www.csupomona.edu/~ajm