When does the relation $V = Ed$ hold?

In my Physics class, we are studying electrostatic potential, and now that we have reached the concept of capacitance, we are using the relation: $$V = Ed$$

We derived it from the definition of potential for an infinite plane, and I understood that perfectly. However, my question is, how come we are also applying it to cables (cylindrical symmetry) and other geometries?

All help appreciated.

In general $V=\int \vec E\cdot d\vec\ell$ so this reduces to $Ed$ when the electric field is constant. In particular, this will not hold for cylindrical geometry since the electric field of a cylinder goes like $1/r$ and is thus NOT constant. Likewise, in the spherical case, the field goes like $1/r^2$ and not not constant either. Indeed, the potentials outside a cylinder and outside a sphere typically go like $\log(r)$ and $1/r$, respectively.