Question
Find the capacitance of the Earth. (Suggestion: The outer conductor of the "spherical capacitor" may be considered as a conducting sphere at infinity where $V$ approaches zero.)
Step 1
Step 1: The capacitance of a spherical capacitor is given by the formula: \[C = \frac{4\pi\epsilon_0R}{k}\] where \(R\) is the radius of the sphere, \(\epsilon_0\) is the permittivity of free space, and \(k\) is Coulomb's constant. Show more…
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Find the capacitance of the Earth. (Hint: The outer conductor of the "spherical capacitor" may be considered as a conducting sphere at infinity where $V$ approaches zero.)
Determine the capacitance of the Earth, assuming it to be a spherical conductor.
Capacitance of the Earth. Consider a spherical capacitor with one conductor being a solid conducting sphere of radius $R$ and the other conductor being at infinity. (a) Use Eq. (24.1) and what you know about the potential at the surface of a conducting sphere with charge $Q$ to derive an expression for the capacitance of the charged sphere. (b) Use your result in part (a) to calculate the capacitance of the earth. The earth is a good conductor and has a radius of 6380 $\mathrm{km} .$ Compare your results to the capacitance of typical capacitors used in electronic circuits, which ranges from 10 $\mathrm{pF}$ to 100 $\mathrm{pF} .$
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