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?