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An infinite cylinder of radius R has a linear charge density λ.
The volume charge density (C/m3) within the cylinder (r ≤ R) is ρ(r) = rρ0/R, where ρ0 is a constant to be determined.
a. Draw a graph of ρ versus x for an x-axis that crosses the cylinder perpendicular to the cylinder axis. Let x range from -2R to 2R.
b. The charge within a small volume dV is dq = ρ dV. The integral of ρ dV over a cylinder of length L is the total charge Q = λL within the cylinder. Use this fact to show that ρ0 = 3λ/2πR2.
c. Use Gauss’s law to find an expression for the electric field strength E inside the cylinder, r ≤ R, in terms of λ and R.
d. Does your expression have the expected value at the surface, r = R? Explain.
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