Integral problem on electric potential

[venom_h]

Homework Statement

A long metal cylinder with radius a is held on the axis of a long, hollow, metal tube with radius b. The inner cylinder has positive charge per unit length \lambda, and the outer cylinder has an equal negative charge per unit length. Calculate the potential V(r) for r<a

Homework Equations

Va-Vb = \intE.dr, where E can be found by Gauss's law

The Attempt at a Solution

My only problem is why the limit for the integral is from a to b even though r < a ??
How does any point r < a experience a potential outside??
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[learningphysics]

If you take the potential at infinity to be 0... then the potential at any radius r is,

V(r) = -\int_{\infty}^r \vec{E}\cdot\vec{dr}

assuming b is the outer radius, and a is the inner radius

V(a) = -\int_{\infty}^a \vec{E}\cdot\vec{dr} = -\int_{\infty}^b \vec{E}\cdot\vec{dr} - \int_{b}^a \vec{E}\cdot\vec{dr}