Wise comments all the way around; I suppose it's a very very very rare
teacher that hasn't messed those signs up publicly in front a class
sometime(s) in there career.
| -----Original Message-----
| From: Forum for Physics Educators [mailto:PHYS-L@lists.nau.edu] On Behalf
| Of John Denker
| Sent: Thursday, February 26, 2004 12:50 PM
| To: PHYS-L@lists.nau.edu
| Subject: Re: Potential of a point charge
|
| I wrote:
| > | Equivalently you could set dr = +ds provided
| > | you write the integral as
| > |
| > | / to r
| > | |
| > | |
| > | / from infinity
| > | . . .
|
| Quoting "RAUBER, JOEL" <JOEL_RAUBER@SDSTATE.EDU>:
| > in order to set dr = + ds, you should integrate from r to infinity,
| > correct?
| >
| > In which case I think you have a typo in the above and should have the
| > limits reversed in the integral.
|
| I suppose it depends on what we think the integrand is (F dot dx
| or -F dot dx) and what we think the integral represents (potential
| gain or potential drop).
|
| In any case, I think Rick's basic point is a good one: There are
| endless opportunities for confusion about the signs. Contributing
| factors include:
| -- you can integrate F dot dx or -F dot dx
| -- you can swap limits of integration
| -- you can calculate potential gain or potential drop
| -- etc......
|
| It's unwise to be dogmatic about the "right" choice at each of
| these steps, because only the product of all the choices matters.
|
| In general, a good rule for staying out of trouble (which I alas
| violated in my previous note) is to write down a complete equation
| (not a fragment) and be absolutely clear about the meaning of all
| the elements of the equation.
|
| ==============
|
| Note: in general, the voltage difference is 1/|r_A| - 1/|r_B|
| for any points A and B whatsoever (except r=0). In particular,
| one point need not be radially outward from the other. So in
| general we must not assume ds=dr or -ds=dr ... rather ds follows
| an arbitrary curvy path between A and B.