Capacitor as big as the Earth

If the Earth were an isolated spherical capacitor, what would be its capacity?

Radius of the Earth is 6400 km.

710 m F 710 mF 710 F 710 F 710 μ F 710 \mu F 710 K F 710 KF

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2 solutions

Rohit Gupta
Jan 2, 2017

The Earth can be treated as an isolated spherical capacitor whose capacitance can be written as 4 π ε 0 R 4\pi {\varepsilon _0}R . Here, R is the radius of the Earth.
Putting the values and solving we get,
C = 710 μ F C=710 \mu F
This shows how large is the unit Farad for capacitance. Even a capacitor of the size comparable to the Earth has the capacity in order of 1 0 4 F 10^{-4} F

Anubhav Tyagi
Jan 2, 2017

Capacitance of an isolated sphere is 4 π ϵ 0 4\pi\epsilon_0 R = 710 micro Faraday

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