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- Thread starter cefarix
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Doc Al

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quasar987

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[tex]\vec{\nabla}\cdot \vec{E} = \frac{\rho}{\epsilon_0}[/tex]

or

[tex]\int \vec{E}\cdot d\vec{a} = \frac{Q_{int}}{\epsilon_0}[/tex]

in integral form.

When we solve it for a charged sphere though, it turns out that E is of a different form inside and outside and is undefined directly at the surface.

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krab

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There is just one equation. However, because the gradient is discontinuous across the surface, when we write the equation as an analytic function, it must be split into two regimes. If this bothers you, realize that if you were to try to find a single continuous function to describe the density rho both inside and outside the sphere, you would end up with the same problem: no way to do it.cefarix said:

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