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Amperes law and electrodynamics and Gauss's law 
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#1
Aug809, 01:32 AM

P: 69

It's evident that ampere's law is used to calculate the magnetic field produced by flowing charges. Can I use Gauss's Law to calculate the electric field produced by the flowing charges also?????
I ask this question because in the middle of a solid conductor, there is a flow of charge. However, in the static case there is no charge in the middle of a solid conductor. So, does Gauss's law inside a solid conductor hold as long as I know how much charge is enclosed at a given time???? 


#2
Aug809, 02:44 AM

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PF Gold
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#3
Aug809, 06:50 PM

P: 69




#4
Aug809, 07:36 PM

Mentor
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Amperes law and electrodynamics and Gauss's law



#5
Aug909, 02:14 AM

P: 669

Gauss law Gives the electric Filed Setup by Stationary Charges Only. And it applies at every case.
Flowing Charges don't produce extra electric Fields, they in fact produce magnetic Filed which is calculated from Amperes law. There are other laws about these. Faraday's Laws Gives the Electric Field Produced By changing magnetic Field and Modified Amperes' law gives magnetic Field produced by changing Electric Field. Moreover like the gauss law in electrostatics there is gauss law for magnetostatics that gives the magnetic Field produced by stationary magnetic charges (poles). 


#6
Aug909, 03:09 AM

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#7
Aug909, 09:47 AM

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#8
Aug909, 01:49 PM

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#9
Aug909, 02:03 PM

P: 1,779

To quote Purcell (Berkeley Physics Course Volume 2, Second Edition, page 175): 


#10
Aug1009, 03:47 AM

P: 669

In fact Gauss Law is always applicable. Since it gives the electric field based on amount of charge enclosed at any instant, we can say it gives instanteneous Electric Field, which is no different than the persistent electric field if uniform current of charge is flowing. Thats why I said moving charges don't produce EXTRA (more than that it would have produced were it at rest) electric Field. 


#11
Aug1009, 07:05 AM

P: 1,779

For OP and future visitors to this thread: Anyway, for the record (in order not to confuse OPs or beginning students of EM theory who might stumble upon this thread), for a good treatment of the fields produced by a charge in motion, refer to Purcell's book (details in my previous post). The pictures in his book are very helpful in understanding the nature of the field patterns. And I would like to state here (for beginning students) that this is a nontrivial subject and so the interpretation of the equations must be made clear, and so must the inputs from experiments be distinguished from the fundamental assumptions made while deriving these expressions. The connection between field transformations and the Lorentz force law must be understood properly. Secondly, ALL classical electrodynamic phenomena can be explained using Maxwell's equations and the Lorentz Force law. So, these equations (of which Gauss's Law is one) are valid in all inertial frames of reference. 


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