The electrostatic potential inside a charged spherical ball is given by `phi=ar^2+b` where r is the distance from the centre and a, b are constants. Then the charge density inside the ball is:

Explanation

Field intensity is along radial line and is
`E_(r ) = (del varphi)/(del r) = -2ar` …(1)
From the Gauss's theorem,
`4pi r^(2) E_(r) = int (dq)/(epsilon_(0))`
where `dq` is the charge contained between the sphere of radii `r` and `r+dr`.
Hence `4pi r^(2) E_(r) = 4pi r^(2) xx (-2ar) = (4pi)/(epsilon_(0)) int_(0)^(r) r^(2) rho (r') dr'` ....(2)
Differentaining (2) `rho = -6 epsilon_(0) a`