Question based on electric flux jee advance 2018

Question

an infinitely long thin non conducting wire is parallel to the axis and carries and uniform line charge density lambda it PSS Earth in non conducting spherical shell of radius r in such a way that are liquid substance and angle 120 degree at the centre of a spherical shell as shown in the figure the probability of free space is a

Answer 1

Consider the diagram.

The charge enclosed by the portion of wire PQ is given by,

Apply Gauss law,

This flux points radially outward from the wire so that the electric field in the direction of z-component is zero and also it is normal to the wire, not to the spherical shell.