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## Homework Statement

Hello,

this is more of a conceptual question than a concrete homework assignment question. I'm learning about Gauss's law and the Prof did an exercise on a sphere with uniform charge distribution, where he found E(r). The trick was, that E(r) was constant over the Gaussian surface he picked. Normally you can't find the integrand of an unknown function if you know the value of the integral, but you can if the function is constant. That enabled him to find E(r).

When he finished he said you cannot deduce E(r) for a non-uniform charge distribution, because E(r) would not be constant so you couldn't pull it out of the integral. I did some research and found exercises where one finds E(r) for a non-uniform charge distribution on a sphere and there are even some posts in this forum on that.

How does this work? E(r) is not constant, right? So how can you find the integrand then?

## Homework Equations

[tex] \oint_S \vec E \cdot \vec{dA}= \frac{Q_{enc}}{\varepsilon_0} [/tex]

## The Attempt at a Solution

My first idea was to construct a Gaussian surface so that E(r) would be constant on it throughout. I mean this should be possible, but the shape of this surface could be weird. This could get arbitrarily complicated though, and one couldn't compute the area of it easily if it was a weird shape...

So I'm stuck and hope you can help me look in the right way.

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