Chapter 3 Fields of Stationary
Electric Charges,II
Solid Angles
Gauss’ Law
Conductors
Poisson’s Equation
Laplace’s Equation
Uniqueness Theorem
Images
Example 1,hollow conductor
the charge on its inner surface is equal to
the charge enclosed within the hollow,
Example 2,isolated charged
conducting plate
Example 3:pair of parallel conducting
plates
They carry charges
of equal magnitude
and opposite signs,
E=0,except btwn
the plates.
Example,solve the Poisson
equation for flat ion beam
(see P75--P78 youself)
This example tells us how to actually
obtain V and E by solving the Poisson
equation,
---a very typical exercise of
mathematical
physics.
3.6 The uniqueness theorem
According to the uniqueness theorem,
the Poisson equation has a unique
solution,V(r),for a given charge density
and for a given boundary conditions.
Mathematicians elaborate very much on
proving this kind of theorems.
We take this theorem as granted.