Register to reply 
Electrostatics  charges in stable equilibriumby gandharva_23
Tags: electrostatics 
Share this thread: 
#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

Sci Advisor
HW Helper
P: 2,002

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

Sci Advisor
HW Helper
PF Gold
P: 2,013

It is called Thomson's theorem.



#4
Mar806, 10:56 AM

Sci Advisor
HW Helper
P: 2,002

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



#5
Mar806, 11:51 AM

Sci Advisor
HW Helper
PF Gold
P: 2,013

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] 


Register to reply 
Related Discussions  
Electrostatics physics help  Classical Physics  8  
Electrostatics calculation help  Introductory Physics Homework  5  
Electrostatics earth problem  Advanced Physics Homework  3  
Reading Smythe's book on static and dynamic electricity  Classical Physics  4  
Doesn't zinc tend to lose e?  Introductory Physics Homework  2 