Consider an electric field $\overrightarrow{\mathit{E}}=E_0\hat{\mathrm{i}},$ where $E_0$ is a constant. The flux through the shaded area (as shown in the figure) due to this field is: 

A wooden block performs SHM on a frictionless surface with frequency, ${\nu }_0$. The block carries a charge $+Q$ on its surface. If now a uniform electric field $E$ is switched-on as shown, then the SHM of the block will be 

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 $K=\frac{1}{4\pi {\epsilon }_0}\frac{q}{L^2}$, which of the following statement (s) is (are) correct? 

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

Charges $Q, 2Q$ and $4Q$ are uniformly distributed in three dielectric solid spheres $1, 2$ and $3$ of radii $\frac{R}{2}, R$ and $2R$ respectively, as shown in the figure. If magnitudes of the electric fields at point P at a distance R from the centre of spheres $1, 2$ and $3$ are $E_1\mathit{,} E_2$ and $E_3$ respectively, then