Daily Physics 350 Problems
2/8 Assignment:
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?
-
a) The electric force is conservative.
-
b) Solutions to Laplace's equation have no local maxima or minima.
-
c) Solutions to Laplace's equation for a given set of boundary
conditions are unique.
-
d) A charge in stable equilibrium would violate the second law of
thermodynamics.
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 woud be a local minimun in the
potential. By Laplace's equation, this connot 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)