A positively charged sphere of radius $r_0$ carries a volume charge density $\rho$ (see figure). A spherical cavity of radius $\frac{r_0}{2}$ is then scooped out and left empty, as shown. $C_1$ is the centre of the sphere and $C_2$ is the centre of the cavity. What is the direction and magnitude of the electric field at point $B$?

      

The figure shows, in cross-section, two solid spheres with uniformly distributed charge throughout their volumes. Each has a radius $R$. The point lies on a line connecting the centres of the spheres, at a radial distance $\frac{R}{2}$ from the centre of the sphere $1$. If the net electric field at a point $P$ is zero, what is the ratio $\frac{q_2}{q_1}$ of the total charges?

Two infinite plane sheets $A$ and $B$ are shown in the figure. The surface charge densities on $A$ and $B$ are $\left(\frac{2}{\mathrm{\pi }}\right)\times {10}^{-9} \mathrm{C} {\mathrm{m}}^{-2}$ and $\left(\frac{-1}{\mathrm{\pi }}\right)\times {10}^{-9} \mathrm{C} {\mathrm{m}}^{-2}$ respectively. $C$, $D$ and $E$ are three points where electric fields (in $\mathrm{N} {\mathrm{C}}^{-1}$) are $E_{\mathrm{c}}$, $E_{\mathrm{D}}$ and $E_{\mathrm{E}}$ respectively.