A capacitor made up of two concentric cylindrical shell or wires separated to each other by a dielectric in between them as shown in the figure below is known as the Cylindrical Capacitor.
Capacitance of Cylindrical Capacitor:
Let, The radius of the inner cylinder be R1 and that of the outer cylinder be R2. And let the relative permittivity of the medium in between the two cylinders be .
Let the charge per meter length of the cable on the outer surface of the inner cylinder be +Q coulomb and on the inner surface of the outer cylinder be -Q coulombs. for all practical purpose, the charge of +Q coulombs/m on the surface of the core can be assumed to be located at it’s axis. The outer cylinder is earthed.
Now,
Surface area of the coaxial cylinder of radius x meters and length of one meter is m2.
Thus, The electrical field intensity at a point x meters away from the center of the inner cylinder is:
or,
Thus, The potential difference developed between the two plates or cylinders in the parallel plate capacitor (V) is:
or,
or,
or,
or,
or,
Or, the capacitance C in the case is:
Thus, The capacitance of a cylindrical capacitor with L meter length or height and R_1 , R_2 the radius of inner and outer cylinder respectively is:
Cylindrical Capacitor Calculator:
Here is a simple Cylindrical Capacitance calculator. Note; You will need to enable javascript for this calculator to work which is enabled in most browsers by default.