A point charge $+Q$ is placed just outside an imaginary hemispherical surface of radius $R$ as shown in the figure. Which of the following statements is/are correct?

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 arc $PQ$ subtends an angle $120°$ 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 (are) true?

An infinitely long solid cylinder of the radius $R$ has a uniform volume charge density $\rho$. It has a spherical cavity of the radius $\frac{R}{2}$ with its centre on the axis of the cylinder, as shown in the figure. The magnitude of the electric field at the point $P$, which is at a distance $2R$ from the axis of the cylinder, is given by the expression $\frac{23\rho R}{16k{\epsilon }_0}$. The value of $k$ is 

An infinitely long uniform line charge distribution of charge per unit length $\lambda$ lies parallel to the $y$-axis in the $y-z$ plane at $z =\frac{\sqrt{3}}{2}a$ (see figure). If the magnitude of the flux of the electric field through the rectangular surface $ABCD$ lying in the $x-y$ plane with the centre at the origin is $\frac{\lambda l}{n{\epsilon }_0}$ (${\epsilon }_0$ is permittivity of free space ), then the value of $n$ is ____.