The diagram shows a small bead of mass $m$ carrying charge $q$. The bead can freely move on the smooth fixed ring placed on a smooth horizontal plane. In the same plane a charge $+Q$ has also been fixed as shown. The potential at the point $\mathrm{P}$ due to $+Q$ is $V$. The velocity with which the bead should projected from the point $\mathrm{P}$ so that is can complete a circle should be greater than

A point charge $+Q$ is placed at point $B$ at a distance $2R$ from the centre $O$ of an uncharged thin conducting shell of radius $R$ as shown in the figure. If $V_{\mathrm{A}}$ be the potential at point $A$, which is at a radial distance of $\frac{R}{2}$ from the centre of the shell, then

Two point charges $q_1$ and $q_2$ are placed in an external uniform electric field as shown in figure. The potential at the location of $q_1$ and $q_2$ are $V_1$ and $V_2$, respectively. The effect of $q_1$ and $q_2$ is not included in $V_1$ and $V_2$, i.e., $V_1$ and $V_2$ are potentials at location of $q_1$ and $q_2$ due to external unspecified charges only. Then electric potential energy for this configuration of two charged particle is

A negative charge is moved by an external agent in the direction of electric field. Then