Spherical Capacitor Calculator, Spherical Capacitance Formula, Calculation

Spherical Capacitor Calculator:

This spherical capacitor calculator will help you find the optimum parameters for designing a spherical capacitor of a specific capacitance.

Unlike the more common parallel-plate capacitor, spherical capacitors consist of two concentric spherical conducting shells separated by a dielectric.

Read on to know about capacitors, spherical capacitor equation and two combinations of spherical capacitors. A capacitor is one of the essential components of an electrical circuit, It stores and releases electricity charges.

Capacitors are widely used in many electronic devices to perform various tasks such as smoothing, filtering or isolating the electrical signal. The construction of capacitors is straightforward – they essentially consist of two separate plates.

To determine the amount of electrical charge a capacitor can store, we use a quantity called capacitance. The more electrical charge a capacitor can hold, the greater its capacitance. To further improve the capacitance, the gap between the plates can be filled with some non-conductive dielectric medium.

Capacitance of a Spherical Capacitor Equation:

Capacitance of a spherical capacitor equation C(F) in Farad is equal to the four pi 4π and multiply the the vacuum permittivity constant ε0(F/m) in farad per meter and multiply the relative permittivity εK and divided by the one divided by the inner radius of the spherical capacitor 1/a(cm) in centimeter and minus the one divided by the outer radius of the spherical capacitor 1/b(cm) in centimeter.Hence the capacitance  of a spherical capacitor formula can be written as

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C(F)= 4π * ε0(F/m) *εK / (1/a(cm) – 1/b(cm))

Where

C = is the spherical capacitor capacitance

A=is the inner radius of the spherical capacitor

B=is the outer radius of the spherical capacitor

ε = is the vacuum permittivity constant and its value is 8.85 *10-12 F/m

εK =is the relative permittivity and its  value is 1

Example:1

A spherical capacitor has an inner sphere radius of 52cm and outer sphere radius of 46cm.Determine the capacitance of the capacitor?

Answer:

Given that

The radius of inner sphere a =52cm=0.52

The radius of the outer sphere b =46 cm=0.46

Capacitance  C= 4π * ε *εK / (1/a – 1/b)

C= (4π *8.85 *10-12 * 1) / (1/0.52 – 1/ 0.46)

C=(1.1121 *10-12) / (0.3557)

C=3.126 *10-12 F

Therefore, the capacitance of the spherical capacitor is 3.126 *1012F

Example:2

A spherical capacitor has an inner sphere radius of 32cm and outer sphere radius of 35cm.Determine the capacitance of the capacitor?

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Answer:

Given that

The radius of inner sphere a =32cm=0.32

The radius of the outer sphere b =35 cm=0.35m

Capacitance  C= 4π * ε*K / (1/a – 1/b)

C= (4π *8.85 *10-12 * 1) / (1/0.32 – 1/ 0.35)

C=(1.1121 *10-12) / (0.267)

C=415.184 *10-12 F

Therefore, the capacitance of the spherical capacitor is 415.184*10-12F

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