An infinitely long thin non-conducting wire is parallel to the $z$-axis and carries a uniform line charge density $\lambda$. It pierces a thin nonconducting spherical shell of radius $R$ in such a way that the arc $P Q$ subtends an angle $120^{\circ}$ at the centre $O$ of the spherical shell, as shown in the figure. The permittivity of free space is $\varepsilon_0$. Which of the following statements is (are) true?
Select ALL correct options:
A
The electric flux through the shell is $\sqrt{3} \mathrm{R} \lambda / \varepsilon_0$
B
The $z$-component of the electric field is zero at all the points on the surface of the shell
C
The electric flux through the shell is $\sqrt{2} \mathrm{R} \lambda / \varepsilon_0$
D
`The electric field is normal to the surface of the shell at all points
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