How Does Electric Field Vary with Distance in a Cylindrical Setup?

[weesiang_loke]

Homework Statement

based on the diagram attached, find the electric field E that varies with r.
the line and the metallic cylindrical shell are infinitely long.
the outer radius of the cylindrical shell is b and the inner one is a
and the line charge density for the line is $$\lambda$$
and the line charge density for the cylindrical shell is $$\lambda$$s

Homework Equations

Gauss's Law ( $$\oint$$E dA = Q_in / $$\epsilon$$

The Attempt at a Solution

by using gauss's law with cylindrical gaussian surface coaxial with the line,
when r < a, i have E = $$\lambda$$ / (2*pi*$$\epsilon$$*r);
for a< r < b, i have E = 0 since the shell is a conductor;

but for r > b, is it E = ($$\lambda$$s + $$\lambda$$) / (2*pi*$$\epsilon$$*r) since the total charge enclosed is the sum of charges in the two bodies?

Pls help me. thanks

 

[vela]

Your calculations are correct.