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Capacitance of the Earth. Consider a spherical capacitor
Chapter 24, Problem 67P(choose chapter or problem)
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 km. Compare your results to the capacitance of typical capacitors used in electronic circuits, which ranges from 10 pF to 100 pF.
Questions & Answers
QUESTION:
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 km. Compare your results to the capacitance of typical capacitors used in electronic circuits, which ranges from 10 pF to 100 pF.
ANSWER:Solution 67P Step 1 of 4: (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. For the spherical capacitor, the capacitance of the capacitor with distance between plates equal to radius is given by, C = 0A d Here d=R 0 A C = R Where is0the permittivity of free space , A is the area of the parallel plates, R is the radius and d is the distance between them.