why is knowing the total charge on the conductors enough?by alemsalem Tags: charge, conductors, knowing 

#1
Jan813, 05:38 PM

P: 159

how do you prove that the electric field is determined uniquely from knowing the total charge on a conductor (just the outline of the proof).
Thanks!! 



#2
Jan813, 10:25 PM

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That will be determined by the properties of the setup. See Maxwell's equations. 



#3
Jan913, 01:39 PM

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The net charge on the conductor is enough.
That is the 'uniqueness theorem' tha is proved in most EM texts. You start with the volume integral of phi grad phi, where phi is the difference of two possible potentials for the same rho (so delsquared phi=0. Then use the divergence theorem. 



#4
Jan913, 05:38 PM

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why is knowing the total charge on the conductors enough?
... and here's me thinking that the electric field is stronger near the pointy bits of a charged conductor... requiring knowledge of the shape of the conductor as well as the net charge.
Perhaps there is a context I'm missing? No doubt you have the right of this question though. 



#5
Jan913, 07:37 PM

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#6
Jan913, 08:14 PM

P: 159

thanks i found the proof in Griffiths, I've seen it along time ago and didn't remember where.
the theorem doesn't say that the electrostatic field doesn't depend on the shape of the conductor, it just says given the total elecrtic charge on the conductors there is only one solution. 



#7
Jan913, 08:25 PM

P: 287

Just to be clear I hope everyone agrees that in electrostatics one can know the electric field around a conductor by knowing:
1) Its shape and 2) Its total charge If not, then I am missing something very important! 



#8
Jan913, 09:08 PM

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The proposition under consideration was:
consider: the field inside a conductor is zero we identify the inside from our knowledge of the conductor's shape if all we know is the total charge, we do not know it's shape therefore, knowledge of the total charge is not sufficient to determine the electric field everywhere. Perhaps if we modify the proposition: the electric field, outside the conductor, is determined uniquely from knowing the total charge on it But the charges could be moving ... lets try again: the electrostatic field, outside the conductor, is determined uniquely from knowing the total charge on it ... now we are getting somewhere  as noted the charges are free to move, and will spread themselves over the surface as far apart as they can from each other. This means they will tend to cluster about ridges and corners  so the field lines about a corner will be denser than the field lines elsewhere. i.e. http://physics.bu.edu/py106/notes/Conductors.html So the electric field outside a needle of charge Q is not going to be, everywhere, the same as the electric field outside a ballbearing of charge Q ... or is it? I think a clear statement about what this particular "uniqueness theorum" is saying would be useful. BTW: it is known by a different name? 



#9
Jan913, 09:09 PM

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#10
Jan913, 09:12 PM

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The point is that given the total charge and the shape of the conductor, there is a unique electrostatic solution—you don't need to be told the charge distribution, since there is only one possible. 



#11
Jan913, 09:35 PM

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No worries.
The OP wording could just have been relying on the context or it could have been due to a misunderstanding. I didn't want to assume ;) Hopefully the question is now answered. 



#12
Jan913, 09:42 PM

P: 159

Yup! thanks!



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