Good point!
Note that the same sort of thing goes into generalizing the E field of a
point charge, E(r) = Q/r^2 to the field of an extended charge, dE = dq/r^2
.
-----Original Message-----
From: Jeffrey Schnick
Sent: Friday, February 16, 2018 8:11 AM
To: Phys-L@Phys-L.org
Subject: [Phys-L] Electric Current
I have a question about electric current. I generally think of the
derivative of something with respect to time as the rate of change of that
something. In the case of a simple circuit such as a resistor connected
across a battery, the current is typically written as I=dq/dt. The question
is, what is the q that is changing? In the case of a different circuit,
where charge is piling up on the plate of a capacitor, it's just the charge
on that capacitor plate; no problem there. But in the case of a resistor
connected across a battery, nothing has the charge q that is changing with
time. We write the expression as if q were a state variable, but nothing
has the corresponding state. It seems that we would be more consistent if
we used a script delta in front of the q the way we do for infinitesimal
amounts of work and heat in thermodynamics.
The best I can come up with is that q represents the total amount of charge
that has crossed a boundary in one of the two possible directions, where the
boundary is the point in the circuit to which the current pertains, and for
charge that has made it all the way around the loop, double counting is
allowed; each time that charge passes through boundary it contributes to the
q. What are your thoughts on this?
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Bob Sciamanda
Physics, Edinboro Univ of PA (Em)
treborsciamanda@gmail.com
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