# Direction of electric field between a pair of parallel plates having a positive charge in the space between them

Two parallel plates are kept in such a way that one is earthed and the other one is held at a potential $$V_1$$. They have a positive charge density $$\rho$$ in the volume between the inner faces of the plates. The distance between the parallel plates is $$d$$. What will be the distribution of potential inside the plates?

First of all, I tried to take a Gaussian surface in the middle of the two plates. At a distance $$x$$ from the centre, the electric field I found out was $$E(r)=4\pi\rho x$$. Now, I can use $$\text{grad} V=-E$$ and $$\text{div} E = 4\pi\rho$$.

But I am confused what will be the direction of the electric field between the plates if there is a positive charge everywhere? Does this mean that the electric field at the centre would be $$0$$?

And if I want to take the plate with $$V=0$$ (i.e. the plate which is earthed) as my $$x=0$$ point and the other plate at $$V=V_1$$ as $$x=d$$, how can I find the electric field then?