Why does the E-field inside a cylinder =0?

[lodovico]

Homework Statement

Figure 24-32 shows a section of a long, thin-walled metal tube of radius R, carrying a charge per unit length  on its surface. Derive expressions for E in terms of distance R from the tube axis, considering both (a) r > R and (b) r < R. Plot your results for the r = 0 to r = 5cm, assuming that  λ= 2*10^-8
C=m//and R = 3cm


[i can't put the figure since the question is in the book]

Homework Equations

q = ε₀ ∫ E dA

The Attempt at a Solution

i got the answer to (a) E=λ/2∏rε₀

i don't understand why (b) is 0

 

[lodovico]

urgent help due tomorrow

 

[haruspex]

You know that field inside a closed conductor, with no internal charges, is 0. You can think of this as being because field lines cannot pass through it. This tube is 'long'; as long as you are not near the ends, any field reaching in from outside will be small.