List of top Physics Questions on Electric Field asked in JEE Advanced

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 $120^{\circ}$ at the centre $O$ of the spherical shell, as shown in the figure. The permittivity of free space is $\in_0$. Which of the following statements is (are) true?

Two non-conducting solid spheres of radii $R$ and $2R$ , having uniform volume charge densities $\rho _1 $ and $ \rho _2 $ respectively, touch each other. The net electric field at a distance $2R$ from the centre of the smaller sphere, along the line joining the centre of the spheres, is zero. The ratio $\rho _1 \, / \, \rho _2 $ can be