tsl105 - V ( a ) = 0 V ( r ) =-Z r a E ( r ) dr =- 2 Z r a...

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Cylindrical Capacitor Conducting cylinder of radius a and length L surrounded concentrically by conducting cylindrical shell of inner radius b and equal length. Assumption: L À b . λ : charge per unit length (magnitude) on each cylinder Q = λL : magnitude of charge on each cylinder Electric field between cylinders: use Gauss’ law E [2 πrL ] = λL ² 0 E ( r ) = λ 2 π² 0 r Electric potential between cylinders: use
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Unformatted text preview: V ( a ) = 0 V ( r ) =-Z r a E ( r ) dr =- 2 Z r a dr r =- 2 ln r a Voltage between cylinders: V V +-V-= V ( a )-V ( b ) = Q 2 L ln b a Capacitance for cylindrical geometry: C Q V = 2 L ln( b/a ) +Q-Q E b a tsl105 p.1/1...
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