An infinitely long thin non-conducting wire is parallel to the \( z \)-axis and carries a unifor...

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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 non-conducting spherical shell of radius \( R \) in such a way that the \( \operatorname{arc} P Q \) subtends an angle \( 120^{\circ} \) at the centre \( O \) of the spherical shell, as shown in the figure. The permittivity of free space is \( \epsilon_{0} \). Which of the following statements is (are) true?
(1) The electric flux through the shell is \( \sqrt{3} R \lambda / \varepsilon_{0} \)
(2) The \( z \)-component of the electric field is zero at all the points on the surface of the shell
(3) The electric flux through the shell is \( \sqrt{2} R \lambda / \varepsilon_{0} \)
(4) The electric field is normal to the surface of the shell at all points
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