Physics 350: Daily Exercise

The following questions questions refer to the material you were to read in preparation for class. Questions one and two require you to write a three or four sentence response. 

 


1.

"Earnshaw's Theorem" states that it is impossible to hold a point charge in stable equilibrium by electrostatic forces alone. Which of the following statements justifies this theorem?


1) a and b, especially b. in order to be in a stable equilibrium, the energy of the charge must be at a minimum, but Laplace's solutions lack minima, they have saddles!

Answers: 1) Statement be justifies the theorem. If a charge was held static by only electrostatic forces, then there would be a local minimum in the potential. By Laplace's equation, this cannot be true

Answers: 1. b) Solutions to Laplace's equation have no local maxima or minima.

Answers: 1.b (i'm not sure on this one)

Answers: 1.b) Solutions to Laplace's equation have no local maxima or minima. 

Answers: 1) the answer is b): solutions to laplace's equation have no local maxima or minima. but in this case, since the problem refers to stable equilibrium, and not to unstable equilibrium, a better statement would simply be that "solutions to laplace's equation have no local minima". wow, i hope i'm right.

Answers: 1. I'm really not sure which of those statements justifies that - but it makes sense to me. Even if you could hold the first charge static with other static charges, you wouldn't be able to keep the others static. Once they start moving, the first one wont be in equilibrium anymore. This probably has to do with the lack of extrema in solutions to Laplace's equation ... 

 

 

Example:  Charge | Potential