# 22.41 A very long, solid cylinder with radius R has positivecharge uniformly distributed throughout it, with charge per unitvolume p. (a) Derive the expression for the electric field insidethe volume at a distance r from the axis of the cylinder in termsof the charge density p. (b) What is the electric field at a pointoutside the volume in terms of the charge per unit length A in thecylinder? (c) Compare the answers to parts (a) and (b) forr = R.(d) Graph the electric-field magnitude as a function of r from3R.r= 0 to r =

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Hint:To check your answers to parts (a) and (b), a correct answer to part (c) should allow you to further write ρ = Q /LπR2, where Q is the total charge on the cylinder and L is the length of the cylinder.

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Step 1

a) Using Gauss law,

Step 2

b) Using Gauss law,

Step 3

c) When r = R,

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