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A long thin straight wire carrying a uniform linear charge density lambda is placed along the axis of a thin hollow metallic cylinder of radius R. The cylinder itself has a net linear charge density of 2*lambda. Assume lambda > 0. Which of the following statements are correct?

1. E(r > R) = 3*lambda / (2*pi*epsilon₀*r) radially outward
2. E(r < R) = 3*lambda / (2*pi*epsilon₀*r) radially outward
3. The linear charge density on the inner surface of the cylinder is -lambda
4. The linear charge density on the outer surface of the cylinder is 3*lambda

Correct answer: E(r > R) = 3*lambda / (2*pi*epsilon₀*r) radially outward

Solution

Inside the conductor E=0 requires the inner surface to carry -lambda (canceling the wire's field). The outer surface carries 3*lambda so total cylinder charge = 2*lambda. For r > R, Gauss's law with total linear charge lambda + 2*lambda = 3*lambda gives E = 3*lambda/(2*pi*epsilon₀*r). Options A, C, and D are all correct; B is incorrect.

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