If the electric potential of the inner shell is $10 \mathrm{V}$ and that of the outer shell is $5 \mathrm{V}$, then the potential at the centre will be, (the shells are uniformly charged.)

 

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,