How do parallel plate capacitors differ from cylindrical ones?

Parallel plate capacitors differ from cylindrical ones in their shape, capacitance formula, and electric field distribution.

Parallel plate capacitors, as the name suggests, consist of two parallel plates separated by a dielectric medium. The capacitance of a parallel plate capacitor is given by the formula C = εA/d, where ε is the permittivity of the dielectric medium, A is the area of one of the plates, and d is the distance between the plates. The electric field in a parallel plate capacitor is uniform and directed from the positive to the negative plate.

On the other hand, a cylindrical capacitor consists of two concentric cylinders. The capacitance of a cylindrical capacitor is given by the formula C = 2πεL/ln(b/a), where ε is the permittivity of the dielectric medium, L is the length of the cylinders, and a and b are the inner and outer radii of the cylinders, respectively. The electric field in a cylindrical capacitor is not uniform and decreases as you move away from the inner cylinder.

The shape of the capacitor affects the distribution of the electric field. In a parallel plate capacitor, the electric field lines are straight and parallel, indicating a uniform electric field. However, in a cylindrical capacitor, the electric field lines are curved, indicating a non-uniform electric field. This difference in electric field distribution can affect the behaviour of the capacitor in an electric circuit.

The capacitance formula also differs due to the shape of the capacitors. The capacitance of a parallel plate capacitor depends on the area of the plates and the distance between them. This means that increasing the area of the plates or decreasing the distance between them will increase the capacitance. However, the capacitance of a cylindrical capacitor depends on the length of the cylinders and the logarithm of the ratio of the outer to the inner radius. This means that increasing the length of the cylinders or decreasing the ratio of the outer to the inner radius will increase the capacitance.

In conclusion, while both parallel plate and cylindrical capacitors store electric charge and energy, their shape leads to differences in their capacitance formula and electric field distribution.