Consider a spherical capacitor with one conductor being a solid conducting spher

Question

Consider a spherical capacitor with one conductor being a solid conducting sphere of radius R and the other conductor being at infinity.

Part A

Use equation C=Q/V 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.

Express your answer in terms of the variables R, Q, and 0.

Part 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.

Explanation / Answer

a)

C = Q/V ( where V is potential difference b/w two conducting surface)

V(sphere) at R = KQ/R

V(sphere) at infinity = 0

=> V = KQ/R

=> C = Q/(KQ/R) = R/K = R*4*pi*0

b)

C = R*4*pi*0

=> C= 6380*10^3*4*3.14*8.85*10^-12 = 0.000709 F OR 709 micro Farad

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