Capacitance of Earth in microfarad | formula value

To find the capacitance of Earth we consider that the Earth is a spherical conductor with radius R and total charge Q. In fact, using this assumption one can determine the capacitance of any planet and satellite like Mercury, Mars, Moon, etc. In this article, we are going to find the capacitance of Earth in microfarad unit. We will develop the formula for capacitance of an isolated spherical conductor and then we will use the parameters of Earth in that equation.

The Formula of capacitance of Earth

Earth and other planets are spherical isolated capacitors. If R and Q be the radius and the charge respectively of the Earth, then the electric potential on the surface of the Earth is, \small {\color{Blue} V=\frac{Q}{4\pi \epsilon _{0}R}}. Where \small \epsilon _{0} is the permittivity of free space.

Now, from the formula of capacitance we know, \small {\color{Blue} C=\frac{Q}{V}}

Then, the capacitance, \small {\color{Blue} C=\frac{Q}{ \frac{Q}{4\pi \epsilon _{0}R} }}

or, the capacitance of the Earth capacitor is, \small {\color{Blue} C=4\pi \epsilon _{0}R} …………..(1) in SI system.

Again, in CGS system, the formula of the capacitance of an isolated sphere like Earth is, \small {\color{Blue} C=R} …….(2)

Capacitance of Earth in microfarad

So, from equation-(1) and equation-(2) it is clear that the capacitance of Earth depends only on its radius.

The radius of the Earth, R = 6400 km = 6.4×10⁶ meter. And, from Coulomb’s force equation in electrostatics we know that, \small 4\pi \epsilon_{0} = \frac{1}{9\times 10^{9}}.

Then the capacitance of Earth, \small {\color{Blue} C=\frac{6.4\times 10^{6}}{9\times 10^{9}}} in Farad.

or, the capacitance of the Earth, C = 0.711×10^-3 Farad.

Now, 1 microfarad = 10^-6 Farad.

So, the Capacitance of Earth in microfarad is C = 711 microfarad.

This is all from this article on the value of Earth’s capacitance in the unit of microfarad. Hope you got your answer. Also, you can determine the capacitance for other planets or satellites like Moon by putting the value of the radius of the planet in equation-(1) or equation-(2). If you still have any doubts on this topic you can ask me in the comment section.

Thank you!

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3. Energy stored in a capacitor.
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