Re: [Phys-L] Electric Current ... short simple version

[John Denker <jsd@av8n.com>]

On 02/16/2018 06:11 AM, Jeffrey Schnick wrote:

> In the case of a simple circuit such as a resistor connected across a
> battery, the current is typically written as 
> I=dq/dt.			[1]

After a couple of long answers, I think I finally
figured out the short and useful answer.

*) Equation [1] is *not* the definition of current.
 It is the conservation/continuity equation.  It
 applies to the total charge q in some region, and
 the total current I flowing into that region.

*) However, it can be used to infer the current in
 wire at some point A, using the following stratagem:

 Insert an imaginary capacitor, with an exceedingly
 large capacitance, in series with the wire, somewhere
 near point A.

 Then construct a region that contains just one of
 the capacitor plates.  The boundary of the region
 passes through the capacitor gap, and also through
 point A.

          . . . . . . .
          .           .
          .           .
          .        |  .  |
          .        |  .  |
  _________________|  .  |____________
         A.        |  .  |
          .        |  .  |
          .        |  .  |
          .           .
          . . . . . . .

 
 Now apply equation [1] to that region.

If I (finally) understand the question, that resolves
all the issues.