Solving Poisson's equation V²p=-Po/&o for the electrostatic potential p(x) in a region with a con charge density Po, two students find different answers, viz. 1 P₁x² and ₂(x) = -₁² The reason why these different 28 solutions are both correct is because &₁(x) = --
Solving Poisson's equation V²p=-Po/&o for the electrostatic potential p(x) in a region with a con charge density Po, two students find different answers, viz. 1 P₁x² and ₂(x) = -₁² The reason why these different 28 solutions are both correct is because &₁(x) = --
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Transcribed Image Text:Solving Poisson's equation V²p=-p /& for the electrostatic potential o(x) in
a region with a con charge density po, two students find different answers, viz.
Q₁ (x)
1 P₁x²
2 &
and 92 (x) = ---P₁²₁ The reason why these different
solutions are both correct is because
(a) space is isotropic and hence x and y are physically equivalent
(b) we can add solutions of Laplace's equation to both (x) and ₂(x)
(c) the electrostatic energy is infinite for a constant charge density
(d) the boundary conditions are different in the two cases
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