You can calculate the capacitance of a spherical capacitor using the following formula: where: b b – Radius of the outer sphere. The relative permittivity \varepsilon_k εk is a constant characteristic for a specific dielectric placed between the capacitor plates.
The capacitance of a spherical capacitor is that of a conducting sphere of radius 'a' surrounded concentrically by a conducting spherical shell of inner radius 'a'. This is the part that answers the question, although the passage also mentions the inner radius 'b'. However, since the question asks for the capacitance of a spherical capacitor without specifying the inner radius, the passage is sufficient as is.
The capacitance for spherical or cylindrical conductors can be obtained by evaluating the voltage difference between the conductors for a given charge on each. By applying Gauss' law to an charged conducting sphere, the electric field outside it is found to be Does an isolated charged sphere have capacitance? Isolated Sphere Capacitor?
Unlike the most common parallel-plate capacitor, spherical capacitors consist of two concentric spherical conducting shells separated by a dielectric. Read on to learn about the capacitors, the spherical capacitor equation, and about two combinations of spherical capacitors.
To find the capacitance of a spherical conductor, the voltage difference between the conductors for a given charge on each must be evaluated. This can be achieved by applying Gauss's law to a charged conducting sphere and integrating the electric field along a radial line to find the voltage between the spheres.
To find the capacitance of a spherical capacitor, first, note down the inner and outer radii. Next, calculate the product of the relative permittivity, vacuum permittivity constants, and 4π. Then, subtract the reciprocal of the outer radius from the reciprocal of the inner radius of the sphere. Finally, divide the product by the subtracted value to obtain the capacitance.