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 $\mathrm{km} .$ Compare your results to the capacitance of typical capacitors used in electronic circuits, which ranges from 10 $\mathrm{pF}$ to 100 $\mathrm{pF} .$

          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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