Figure shows three concentric conducting spherical shells of radii $a, b$ and $c\left(c>b>a\right).$ The innermost and outermost shell are given charges $Q_1$ and $Q_2$ respectively, and the middle shell has been earthed. Select the correct alternative(s).

Two non-conducting spheres of radii $R_1$ and $R_2$ and carrying uniform volume charge densities $+\mathrm{\rho }$ and $-\mathrm{\rho }$, respectively, are placed such that they partially overlap, as shown in the figure. At all points in the overlapping region

Six point charges are kept at the vertices of a regular hexagon of side $L$ and centre $O,$ as shown in the figure. Given that $K=\frac{q}{4\pi {\epsilon }_0{L}^2},$ which of the following statement(s) is/are correct?

A parallel plate capacitor has a dielectric slab of dielectric constant $K$ between its plates that covers $\frac{1}{3}$ of the area of its plates, as shown in the figure. The total capacitance of the capacitor is $C$ while that of the portion with dielectric in between is $C_1.$ When the capacitor is charged, the plate area covered by the dielectric gets charge $Q_1$ and the rest of the area gets charge $Q_2.$ The electric field in the dielectric is $E_1$ and that in the other portion is $E_{2^{·}}$ Choose the correct option/ options, ignoring edge effects.

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?