Problem 26.40 A spherical capacitor consists of two concentric conducting spheri

Question

Problem 26.40

A spherical capacitor consists of two concentric conducting spherical shells of radii R and 6 R .

Part A

How long would a coaxial cylindrical capacitor made of two concentric cylindrical conductors of radii R and 5 R have to be in order to have the same capacitance as the spherical capacitor?

Express your answer using three significant digits.

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Part B

What plate separation distance would be required for a parallel-plate capacitor made of two circular conductors each of radius R in order to have the same capacitance as the spherical capacitor?

Express your answer using three significant digits.

Explanation / Answer

capacitance of spherical capacitor=4*pi*epsilon*(R*6R/(6R-R))=4*pi*epsilon*6R/5

capacitance of cyllindrical capacitor=2*pi*epsilon*L/ln(5R/R)

equation both we got

2*pi*epsilon*L/ln(5R/R)=4*pi*epsilon*6R/5

L=2ln5*6/5=3.86R

(b)

capacitance=epsilon*pi*R^2/d=4*pi*epsilon*6R/5

d=0.208R

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