A spherical capacitor consists of two concentric conducting spherical shells of radii R1 (inner shell) and R2 (outer shell). The shells have equal and opposite charges of +Q and −Q, respectively. For an isolated conducting spherical capacitor, the radius of the outer shell can be considered to be infinite.
Conventionally, considering the symmetry, the electric field between the concentric shells of a spherical capacitor is directed radially outward. The magnitude of the field, calculated by applying Gauss’s law over a spherical Gaussian surface of radius r concentric with the shells, is given by,
![Equation1](/files/ftp_upload/13735/13735_Equation_PT_1.svg)
Substitution of the electric field into the electric field-capacitance relation gives the electric potential as,
![Equation2](/files/ftp_upload/13735/13735_Equation_PT_2.svg)
However, since the radius of the second sphere is infinite, the potential is given by,
![Equation3](/files/ftp_upload/13735/13735_Equation_PT_3.svg)
Since, the ratio of charge to potential difference is the capacitance, the capacitance of an isolated conducting spherical capacitor is given by,
![Equation4](/files/ftp_upload/13735/13735_Equation_PT_4.svg)
A cylindrical capacitor consists of two concentric conducting cylinders of length l and radii R1 (inner cylinder) and R2 (outer cylinder). The cylinders are given equal and opposite charges of +Q and –Q, respectively. Consider the calculation of the capacitance of a cylindrical capacitor of length 5 cm and radii 2 mm and 4 mm.
The known quantities are the capacitor’s length and inner and outer radii. The unknown quantity capacitance can be calculated using the known values.
The capacitance of a cylindrical capacitor is given by,
![Equation5](/files/ftp_upload/13735/13735_Equation_PT_5.svg)
When the known values are substituted into the above equation, the calculated capacitance value is 4.02 pF.