Capacitance in code

You will write four small functions about capacitors. They use $Q = CV$, $C = \varepsilon_0 A/d$ and $C = 4\pi\varepsilon_0\,ab/(b - a)$.

The idea. A parallel-plate capacitor in air has $C = \varepsilon_0 A/d$. Two concentric spheres of radii $a$ and $b$ have $C = 4\pi\varepsilon_0\,ab/(b - a)$. Every length is in metres, every capacitance in farad.

Your tasks.

1. In charge, return the charge in coulomb on a capacitor C charged to a voltage V.
2. In plate_capacitance, return the capacitance of two square plates of a given side, a given gap apart, in air.
3. In plate_gap, return the gap that gives a capacitance C with square plates of a given side.
4. In sphere_capacitance, return the capacitance of a ball of radius a inside a shell of inner radius b.