Electric potential for concentric spheres and charged surface [closed]

Question

A few conceptual questions about a charged sphere inside an initially neutral spherical shell and about uniform E for a charged plane.

1. How would I go about calculating potential at a certain point in space without a potential value at a reference point? I know that there is a constant added on if you do an indefinite integral right from the start to find $V(X)$, but how does this relate to this situation? I'm mainly confused on the difference between finding delta v and v through integration.

   I know that $\Delta V$ = $\int_a^x \! E \, \mathrm{d}x$ where $x$ is the point I'm trying to calculate the potential at and a is the reference point. $\Delta V = V(x)-v(a)$. So, for the sake of a shorter equation, I assume that $E$ is uniform and in this example is for a surface: $E = \sigma/ \epsilon_0$. If I substitute this into the $\delta V$ equation and evaluate the 'definite' integral I get $V(x)-V(a) = -(\sigma/\epsilon_0 x-\sigma/\epsilon_0 a)$. I am looking for $V(X)$ so I add $V(A)$ to the other side of the equation but it doesn't cancel with anything and i'm left with 2 times the potential at the reference point. Why?

2. Assuming that a charged sphere is inside a neutral spherical shell. How would I go about finding the potential at a radius that is between the inner sphere and the inner surface of the spherical shell. I know that the potential for a point charge is $kq/r - kq/a$ where $a$ is the reference point, usually set at x$ = \infty$ since that is where $V=0$. But I can't use this reference point at this radius. So how would I find the potential here?

Answer 1

From (B): the reference point is not at the radius. You must find the potential of the charged sphere hull with the center of the sphere as reference, or a smaller imaginary sphere between the center and the sphere hull (of course this depends on what that sphere actually suppose to represent, if it's not only a theoretical model). You do not need to compare the sphere hull/shell potential to that of the neutral larger sphere, because you already stated that the big sphere is neutral, so you could even use that as reference if you need.

Which brings us to (A), where you over-complicated things. If your sphere is charged (known charge) and you take the reference zero-value as the center or even the big neutral hull (which also will be considered zero), you can correctly determine the potential in any other point inside or outside the sphere hull.