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Electrostatics  charges in stable equilibriumby gandharva_23
Tags: electrostatics 
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#1
Mar806, 05:01 AM

P: 62

We have a charge distribution in which all the charges are in equilibrium due to electrostatic forces . Can we prove that none of these charges will be in stable equilibrium ?



#2
Mar806, 06:18 AM

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Yes, since the potential due to the other charges satisfies [itex]\nabla^2 V=0[/itex]. V is harmonic with has the property that is has no local maxima or minima.



#3
Mar806, 10:27 AM

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PF Gold
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It is called Thomson's theorem.



#4
Mar806, 10:56 AM

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Electrostatics  charges in stable equilibrium
Do you mean Earnshaw's theorem?



#5
Mar806, 11:51 AM

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PF Gold
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Whoops, Galileo is right again. I meant Earnshaw.
Thomson had several theorems (besides his home run), but not that one. Sorry, and thank you. 


#6
Mar806, 09:48 PM

P: 62

Yes, since the potential due to the other charges satisfies [itex]\nabla^2 V=0[/itex]is being generated. Reload this page in a moment.. V is harmonic with has the property that is has no local maxima or minima.
thats what i wanted to ask . how can we prove that [itex]\nabla^2 V=0[/itex] 


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