$A$ long, straight wire is surrounded by a hollow, thin, long metal cylinder whose axis coincides with that of the wire. The wire has a charge per unit length of $\lambda$, and the cylinder has a net charge per unit length of $2\lambda$. The radius of the cylinder is $R$. Which of the following statements is correct?

• A
  Surface charge density on the inner surface of the cylinder is $-\frac{\lambda}{2\pi R}$.
• B
  Surface charge density on the outer surface of the cylinder is $\frac{3\lambda}{2\pi R}$.
• C
  The electric field outside the cylinder at a distance $r$ from the axis is $\frac{3\lambda}{2\pi \epsilon_0 r}$.
• D
  The electric field outside the cylinder at a distance $r$ from the axis is $\frac{2\lambda}{\pi \epsilon_0 r}$.