Capacitance of Spherical and Cylindrical Capacitors Capacitance is a measure of a capacitor's ability to store electric charge. It is typically defined as th...
Capacitance is a measure of a capacitor's ability to store electric charge. It is typically defined as the ratio of the total charge stored on the capacitor to the potential difference across its terminals.
Spherical capacitors
A spherical capacitor is a spherical shape made of a conductor with a constant charge density. Due to the symmetry, the electric field lines inside a spherical capacitor are also spherical and have the same magnitude.
The capacitance of a spherical capacitor with a radius r is given by:
where q is the total charge stored on the capacitor.
Cylindrical capacitors
A cylindrical capacitor is a cylinder with a constant charge density. The electric field lines inside a cylindrical capacitor are also cylindrical and have the same magnitude.
The capacitance of a cylindrical capacitor with a length l and a radius r is given by:
where L is the length of the cylinder.
Comparing the two types of capacitors
Both spherical and cylindrical capacitors have the same capacitance per unit charge, but the values are different due to their specific shapes.
Examples
A spherical capacitor with a radius of 10 cm has a capacitance of 100 nF.
A cylindrical capacitor with a length of 20 cm and a radius of 5 cm has a capacitance of 250 nF