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 = $$\int$$E.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

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