Prove the capacitance formula of a spherical capacitor

How do you calculate the capacitance of a spherical capacitor?

The equation shows that to calculate the capacitance of a spherical capacitor formula, take the radii of the outer and inner spheres and the medium between the spheres. If the radius of the outer conductor is taken to infinity, the equation would be;

How do you find the capacitance of a sphere?

For more such interesting formulas and concepts subscribe BYJU’S YouTube Channel!! The capacitance of the Spherical Capacitor is found by analysing the voltage difference between the conductors for a given charge on each, It also depends on the inner and outer radius of each sphere.

What is a spherical capacitor?

A spherical capacitor consists of a solid or hollow spherical conductor, surrounded by another hollow concentric spherical of different radius. A spherical capacitor formula is given below: Where, C = Capacitance Q = Charge V = Voltage r 1 = inner radius r 2 = outer radius ε 0 = Permittivity (8.85 x 10 -12 F/m)

How to construct a spherical capacitor?

As mentioned earlier capacitance occurs when there is a separation between the two plates. So for constructing a spherical capacitor we take a hollow sphere such that the inner surface is positively charged and the outer surface of the sphere is negatively charged. The inner radius of the sphere is r and the outer radius is given by R.

Do spherical capacitors have a radius?

Since spherical capacitors have a radius, the introduction of spherical capacitance involves its charge and potential difference and can be directly proportional to its radius. But the radius can be for the inner and outer surface, so the calculation changes accordingly for capacitance.

What is the equivalent capacitance of a spherical capacitor?

The equivalent capacitance for a spherical capacitor of inner radius 1r and outer radius r filled with dielectric with dielectric constant It is instructive to check the limit where κ , κ → 1 . In this case, the above expression a force constant k, and another plate held fixed.