Slabs and dielectrics in code

You will write four functions that follow a dielectric slab in a capacitor.

The idea. A dielectric of constant $K$ that fills the gap multiplies the capacitance by $K$. A slab of thickness $t$ that fills part of the gap gives $C = \varepsilon_0 A/(d - t + t/K)$. A metal slab gives $C = \varepsilon_0 A/(d - t)$. Every length is in metres.

Your tasks.

1. In charge_battery_on, return the charge after a dielectric fills the gap of a capacitor C0 that stays joined to a battery of voltage V.
2. In voltage_battery_off, return the voltage after the dielectric goes in, when the battery was removed before and the voltage was V0.
3. In slab_capacitance, return the capacitance of plates of area area and gap gap with a slab of thickness t and constant K.
4. In metal_slab_capacitance, return the same for a metal slab of thickness t.