The volumetric charge density of a cylinder of radius R is proportional to the distance to the center of the cylinder, that is, ρ = Ar when r≤R, with A being a constant. (a) Sketch the charge density for the region - 3R < r < 3R. What is the dimension of A? b) Calculate the electric field for a point outside the cylinder, r > R c) Calculate the electric field for a point inside the cylinder, r

The volumetric charge density of a cylinder of radius R is proportional to the distance to the center of the cylinder, that is, ρ = Ar when r≤R, with A being a constant. (a) Sketch the charge density for the region - 3R < r < 3R. What is the dimension of A? b) Calculate the electric field for a point outside the cylinder, r > R c) Calculate the electric field for a point inside the cylinder, r

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter25: Gauss’s Law

Section: Chapter Questions

Problem 43PQ: The nonuniform charge density of a solid insulating sphere of radius R is given by = cr2 (r R),...

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Electric Charges and Fields

One of the fundamental properties is the electromagnetic property. Charge cannot be destroyed by any process and this contributes formally to the law of charge conservation.

Question

The volumetric charge density of a cylinder of radius R is proportional to the distance to the center of the cylinder, that is, ρ = Ar when r≤R, with A being a constant.

(a) Sketch the charge density for the region - 3R < r < 3R. What is the dimension of A?
b) Calculate the electric field for a point outside the cylinder, r > R
c) Calculate the electric field for a point inside the cylinder, r<R.
d) Sketch Exr

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Step 1: Determine the given data:

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Step 2: (a) Sketch the charge density for the region - 3R < r < 3R and find the dimension of A:

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Step 3: b) Calculate the electric field for a point outside the cylinder, r > R:

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Step 4: c) Calculate the electric field for a point inside the cylinder, r<R.

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Step 5: d) Sketch E vs r:

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