Consider a hollow spherical conductor of inner radius a and outer radius 3a. The conductivity (sigma) is a function of r, measured from the center of the sphere: sigma = c / r, where a < r < 3a and c is a constant. a) If we apply a potential difference V between it's inner and outer surfaces, with the inner surface at a higher potential, find the resulting current density j and the electric field E as a function of r. b) Find the resistance R of the spherical resistor

Consider a hollow spherical conductor of inner radius a and outer radius 3a. The conductivity (sigma) is a function of r, measured from the center of the sphere: sigma = c / r, where a < r < 3a and c is a constant. a) If we apply a potential difference V between it's inner and outer surfaces, with the inner surface at a higher potential, find the resulting current density j and the electric field E as a function of r. b) Find the resistance R of the spherical resistor

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter28: Current And Resistance

Section: Chapter Questions

Problem 68PQ

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Concept explainers

Resistivity

Resistivity is a characteristic property of the conductor’s material that measures the extent to which the material opposes the flow of current. It is denoted by the Greek letter “rho”. Electrical resistivity, also known as specific resistance, depends on the nature of the material of the conductor and is unaffected by its dimensions.

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a) If we apply a potential difference V between it's inner and outer surfaces, with the inner surface at a higher potential, find the resulting current density j and the electric field E as a function of r.

b) Find the resistance R of the spherical resistor

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