Re: Proof of Ohms law
- From: "Jon Slaughter" <Jon_Slaughter@xxxxxxxxxxx>
- Date: Wed, 06 Feb 2008 00:35:21 GMT
"noone." <harrytuttle777@xxxxxxx> wrote in message
news:foao1t024g6@xxxxxxxxxxxxxxxxxxxxxxx
Has anyone ever proven Ohms law from first principals?
I mean is there any way to take the laws of electrostatics, and from the
derive E = IR?
Just Curious
-Thanks
It can be proved from maxwell's equations(and chances are any book on
electromagnitism will drive it). Also there are a few assumptions that are
made.
Heres the general idea:
J = -ne*v is the current density for a material with charge moving on
average with speed v.
but v = - (e/m)E*tau
So J = g*E where g is called the conductivity. i.e., it depends on the
material only and not the applied field E.
Hence there is a relation between the voltage and current(density) and it
says they are proportional(For the assumption on the average velocity).
If you apply it to a "rod" or "wire" then you get the macroscopic version
which is ohms law.
The main idea here is that applying an electric field produced a motion of
charge.. e.g., a velocity of charge and hence v is a function of E. But
current is just the motion of these charges and hence ultimately I is a
function of E. For many materials its simply proportionate because v is
proportionate to E. Its not always the case and of course fails for
sufficiently large fields and even depends on frequency(which isn't taken
into consideration for this simple analysis). (although the concept can be
applied in those cases too by using it as a linear approximation)
.
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