The figure shows a solid hemisphere with a charge of$5 \mathrm{nC}$ distributed uniformly throughout its volume. The hemisphere lies on a plane and point $P$ is located on the plane along a radial line from the centre of curvature at a distance of $15 \mathrm{cm}.$The electric potential at a point $P$ due to the hemisphere is,

 

A uniform electric field of $400 \mathrm{V} {\mathrm{m}}^{-1}$ exists in space as shown in the graph below. Two points $A$ and $B$ are also shown with their co-ordinates. The potential difference $V_{\mathrm{B}}-V_{\mathrm{A}}$ is

An electric dipole is placed in a uniform electric field $\overrightarrow{E}$ of magnitude $40 \mathrm{N} {\mathrm{C}}^{-1}$. The graph shows the magnitude of the torque on the dipole versus the angle $\mathrm{\theta }$ between the field $\overrightarrow{E}$ and the dipole moment $\overrightarrow{p}$. The magnitude of dipole moment $\overrightarrow{p}$ is equal to

The electric potential between a proton and an electron is given by $V=V_0\ln \frac{r}{r_0}$ where $r_0$ is a constant. What will be the variation of $r_n$ with $n$, $n$ being the principal quantum number, assuming Bohr’s model to be applicable,