A hollow thin-walled glass tube of length $L$, is open at one end while the other end is closed by a hollow thin-walled glass hemisphere of radius $R$. The axis of the tube is along the $x$-axis with the open end at the origin, as shown in the figure. A net positive charge $Q$ is distributed uniformly over the entire surface with surface charge density $\sigma$. The magnitude of the electric field at $O$ due to the hemisphere is $\sigma / 4 \epsilon_0$. Choose the correct statement(s).

• Correct answer
  A

  If $L=R$, then the direction of electric field at $O$ is $-\hat{i}$.
• B

  The surface charge density $\sigma=\frac{Q}{2 \pi R(L+2 R)}$
• Correct answer
  C

  At a point $x \gg L, R$, the magnitude of the electric field is proportional to $1 / x^2$.
• Correct answer
  D

  When $L=\sqrt{3} R$, the electric field at $O$ is zero.

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