Formulas/Concepts Used:

Capacitance:

If two conductors have a potential difference V between the them and have charges Q and -Q respectively on them, then their capacitance is defined as

Capacitance of a Capacitor in presence of a dielectric:
The capacitance of the capacitor is initially C₀ and then a dielectric medium of dielectric constant K is inserted between the plates. The new capacitance is

Also for parallel plate capacitors,

Where ϵ0 is the permittivity of free space, A is the area of plate and l is the distance between the plates.

Charging a capacitor:

A capacitor of capacitance C is being charged using a battery of emf ϵ through a resistance R . A switch S is also connected in series with the capacitor. The switch is initially open. The capacitor is uncharged at first. At t=0, the switch is closed. The current through the circuit at anytime t>0 is given by:

Where I₀ is the initial current.

The charge is given by:

Note that is known as time constant.

Given,

Area of the plate,

(

Now, distance of separation:

Emf of battery,

Resistance ,

Time,

Now,

Time constant,

We want to find the charge on the capacitor at t = 10ns

Now,