(Solved): 40. \( \quad \bullet \) INT CALC An infinitely long cylinder of radius \( R \) has linear charge d ...

40. \( \quad \bullet \) INT CALC An infinitely long cylinder of radius \( R \) has linear charge density \( \lambda \). The potential on the surface of the cylinder is \( V_{0} \), and the electric field outside the cylinder is \( E_{r}=\lambda / 2 \pi \epsilon_{0} r \). Find the potential relative to the surface at a point that is distance \( r \) from the axis, assuming \( r>R \).