JEE Advanced · 2018 · 20 May 2018 · Paper 2 · Electrostatics

The charge enclosed by the spherical shell is the charge on the wire segment inside it. The length of this segment is $2R\cos 30^{\circ }=2R\cdot \frac{\sqrt{3}}{2}=\sqrt{3}R$. Therefore, the enclosed charge is $q=\lambda \cdot \sqrt{3}R$. By Gauss's law, the electric flux is $\Phi =\frac{q}{{ϵ}_0}=\frac{\sqrt{3}R\lambda }{{ϵ}_0}$ (A is correct, C is incorrect). The electric field from an infinite line charge is radial (perpendicular to the wire), so it has no component along the $z$-axis (B is correct). The field is not normal to the spherical surface at all points (D is incorrect).