A displacement current calculator

You will write three small functions for a capacitor that is being charged. Use $\varepsilon_0 = 8.85 \times 10^{-12}\ \text{C}^2/(\text{N m}^2)$.

The idea. Parallel plates of area $A$ and gap $d$ have $C = \varepsilon_0 A/d$. The displacement current in the gap is $I_d = C\,dV/dt$. For circular plates of radius $R$ carrying a charging current $I$, the magnetic field at a distance $r$ from the axis is $B = \mu_0 I r/2\pi R^2$ inside, and $B = \mu_0 I/2\pi r$ outside, with $\mu_0/2\pi = 2 \times 10^{-7}$ T m/A.

Your tasks.

1. In capacitance, return the capacitance in F of parallel plates of area area in m² and gap gap in m.
2. In displacement_current, return the displacement current in A for a capacitance cap in F and a voltage that changes at dv_dt in V/s.
3. In field_between_plates, return the magnetic field in T at a distance r from the axis, for plates of radius radius, charged by current. All lengths are in m.