Calculate the capacitance of the Earth (tau_Earth 6378 km). In class we discusse

Question

Calculate the capacitance of the Earth (tau_Earth 6378 km). In class we discussed an ever-present electric field called the "Fair Weather Electric Field" that points radially outward from the Earth's surface. At the Earth's surface this field has a magnitude of about E = 300 Volts/meter. In class, we used Gauss's Law to find that the total charge Q on the surface of the Earth is approximately Q = 1.36 Times 10^6 Coulombs. calculate the total energy stored in this field by integrating the field in spherical coordinates over all space from tau_Earth rightarrow infinity.(r

Explanation / Answer

here,

capacitance of a spherical conductor is , C = 4*(pi) * e0 * R

as radius of earth is ,R = 6 * 10^6

therefore the its capacitance is equal ,

C = (1/(9 * 10^9)) * 6 * 10^6

C = 0.7 * 10^ -3 F

the capacitance of earth is 0.7 * 10^ -3 F

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