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The field potentail in a certain region...

The field potentail in a certain region of space depends only on the `x` coordinate as `varphi = -ax^(3) + b`, where `a` and `b` are constants. Find the distribution of the space charge `rho (x)`.

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Field intensity along x-axis.
`E_(x) = (del varphi)/(del x) = 3 a x^(2)` ….(1)
Then using Gauss's theorem in differential from
`(del E_(x))/(del x) = (rho (x))/(epsilon_(0))` so, `rho(x) = 6a epsilon_(0) x`.
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