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  1. K

    Do electric fields in a conductor go to zero in all instances?

    As far as I understand, such a charge distribution (a) always exists; and (b) is unique. This is a boundary value problem for Poisson's equation and existence and uniqueness of solutions (given completely specified boundary conditions) is a theorem.
  2. K

    Variance in particle number

    \langle N \rangle is the Fermi-Dirac distribution, which is derived on that wikipedia page. So, you can perform the derivative yourself and verify the second equality. The first equality can be derived as follows. First, \displaystyle \langle ( \Delta N )^2 \rangle = \langle (N - \langle N...