The electrostatic potential in the region between two long coaxial cylinders of radii $a$ and $b$ is given by $\phi=\alpha \ln (r / a)+\beta$, where $\alpha$ and $\beta$ are constants. Here, $\alpha \gt 0$ and $r$ denotes radial distance from the axis such that $a \lt r \lt b$. Then, the correct option $(s)$ is (are)

• Correct answer
  A

  The charge per unit length on the inner cylinder is $-\left(2 \pi \epsilon_0 \alpha\right)$.
• B

  Capacitance per unit length is $\ln (b / a) /\left(2 \pi \epsilon_0\right)$.
• C

  The charge density on the outer cylinder is $-\left(\epsilon_0 \alpha\right) / b^2$.
• Correct answer
  D

  The electric field in the region between two cylinders is $-(\alpha / r) \hat{r}$.

Hence, the correct answer is options: 'A', 'D'.