Suppose a capacitor consists of two coaxial thin cylindrical conductors. The inner cylinder of radius rg has a charge of +Q, while the outer cylinder of radius r, has charge -Q. Theelectric field E at a radial distance r from the central axis is given by the function:E = ae-T/ao + B/r + bowhere alpha (a), beta (8), ao and bo are constants. Find an expression for its capacitance.First, let us derive the potential difference Vab between the two conductors. The potential difference is related to the electric field by:Voh =EdEdrCalculating the antiderivative or indefinite integral,Vab = (-aaoe-r/a0 + B+ boBy definition, the capacitance Cis related to the charge and potential difference by:C =Evaluating with the upper and lower limits of integration for Vab, then simplifying:C = Q/((erb/ao - eralao) + ß In() + bo ())

The given electric field is, Here, a0, b0, ?, and β are constants. The potential difference between…

Suppose a capacitor consists of two coaxial thin cylindrical conductors. The inner cylinder of radius ra has a charge of +Q, while the outer cylinder of radius rh has charge -Q. The electric field E at a radial distance r from the central axis is given by the function: E = ae-r/ao + B/r + bo where alpha (a), beta (8), ao and bo are constants. Find an expression for its capacitance.

Suppose a capacitor consists of two coaxial thin cylindrical conductors. The inner cylinder of radius ra has a charge of +Q, while the outer cylinder of radius rh has charge -Q. The electric field E at a radial distance r from the central axis is given by the function: E = ae-r/ao + B/r + bo where alpha (a), beta (8), ao and bo are constants. Find an expression for its capacitance.

University Physics Volume 2

18th Edition

ISBN:9781938168161

Author:OpenStax

Publisher:OpenStax

Chapter7: Electric Potential

Section: Chapter Questions

Problem 75P: The probability of fusion occurring is greatly enhanced when appropriate nuclei are brought close...

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