Find the electric field strength vector at the centre of a ball of raiduius `R` with volume charge density `rho implies ar`, where `a` is a constant vector, and `r` is a radius vector drawn from the ball's centre.

Explanation

Let us consider an elemental spherical shell of thickness `dr`. Thus surface charge density of the shell `sigma = rho dr = (vec(a). vec(r )) dr`.
Hence the sougth field strength
`vec(E) = - (vec(a))/(3 epsilon_(0)) int_(0)^(R ) r dr = (vec(a) R^(2))/(6 epsilon_(0))`