If you have two parallel plates of opposite charge with a dielectric in between, then
Capacitance $$ C = \dfrac{A \epsilon_{0}}{d} K$$
Where $ K $ is the dielectric constant.
This is used to calculate the capacitance of a capacitor. However, a real capacitor is actually two of those plates rolled up many times. Wouldn't the electric field $ \vec{E} $ be different?
So why is the equation for the capacitance still valid?
Best Answer
You can still use this formula if the parallel plates are rolled enough times so that the curvature of the plates is minimal. Therefore, this formula still holds. Remember that this formula, even in the case of real parallel plates, requires that $A >> d$. So, it is not exact. There is also the boundary problem: close to the boundary of the capacitor $\vec{E}$ is not perpendicular to the plates.
All this to say that this equation is an approximation. How good of an approximation it is? That's an engineering question. In the lab, $C$ depends on the $\frac{A}{d}$ ratio, the magnitude of V, and yes, on the curvature of the plates, in case they are rolled up.