Question

Two 0.25 cm radius coins are separated by a 0.1 mm thick piece of paper with dielectric constant kappa = 6.475. They form a capacitor. A 8 V battery is connected to the capacitor. How much charge is stored on each coin? The area of a circle is given by pi r^2. C

Answer 1

This is a practical example of a parallel-plate capacitor.

The capacitance of a parallel-plate capacitor with a dielectric in between it is given by

We will calculate each of the quantites in the formula in terms of their SI units.

Here, the area is the area of overlap between the two plates, i.e its the area of a single plate that is considered.

We are expressing the radius in terms of metres and not centimeters in the following calculation

The distance between the plates is given as

We are also given the dielectric constant,

Substituting our values, we get

Now,we have the capacitance. Given that we attach it to a battery, equal and opposite charges develop on the plates. The magnitude of the charge on either of the plates is given by the formula

The negative of this charge will be present on the negative plate, and the postive of this will be present on the positive plate.