Educator

Calculating Capacitance

• Isolated conducting sphere: may be taken as a capacitor if we imagine that there is a spherical conducting shell at infinity. In this case, C = 4*pi*epsilon_0*R, where R is the radius of the sphere.
• Spherical capacitor: composed of a conducting sphere of radius a surrounded by a spherical conducting shell of radius b. To find C, we put +Q on the sphere, -Q on the shell, and calculate the potential difference V. Then C = Q / V. We find that the capacitance is given by C = 4*pi*epsilon_0*a*b / (b – a).
• Parallel-plate capacitor: C = epsilon_0 * A / d, where A is the plate area and d is the separation between the plates.
• Cylindrical capacitor: A conducting cylinder of radius a surrounded by a coaxial cylindrical sheel of radius b. The capacitance per unit length is

  C / L = 2*pi*epsilon_0 / ln(b / a)