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Re: [Phys-L] Electric Current ... including steady current in a loop





-----Original Message-----
From: Phys-l [mailto:phys-l-bounces@mail.phys-l.org] On Behalf Of Robert
Cohen
Sent: Friday, February 16, 2018 4:36 PM
To: Phys-L@Phys-L.org
Subject: Re: [Phys-L] Electric Current ... including steady current in a loop

On Friday, February 16, 2018 2:28 PM, Jeffrey Schnick wrote:

But to say that one part of the flow of something through a closed
surface, or the flow of something through an open surface, is the rate
of change in the amount of that something, bothers me; I can live with it
though.
I was hoping I was missing something.

To me, they are two different usages of "dq" that happen to be equal in this
case. :)

Just curious -- are you also bothered by figuring out the total mass of a ball by
cutting it into pieces of mass dm and then integrating? In other words, does
the use of "dm" bother you because there isn't a quantity m that is
undergoing change during the integration?

No, but your curiosity has helped to make your point, and I think it's a good one. I think you are saying that in the continuity equation,
I_net = dq/dt,
the dq/dt is the time rate of change of the total amount of charge in a closed region of space, but in what many put down as the definition of current,
I = dq/dt,
the dq/dt is the following quotient: (the amount of charge that crosses a boundary in a time interval of duration dt), divided by dt.
In other words, in one case the dq is the change in the total amount of charge in a region of space, and in the other case, the dq is just a little bit of charge.




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