Two charges of magnitude $5\, nC$ and $-2\, nC$, one placed at points $(2\, cm, 0, 0)$ and $(x\, cm, 0, 0)$ in a region of space, where there is no other external field. If the electrostatic potential energy of the system is $ - 0.5\,\mu J$. The value of $x$ is.....$cm$

A point charge $q$ is surrounded by eight identical charges at distance $r$ as shown in figure. How much work is done by the forces of electrostatic repulsion when the point charge at the centre is removed to infinity?

As shown in figure, on bringing a charge $Q$ from point $A$ to $B$ and from $B$ to $C$, the work done are $2\, joule$ and $-3\, joule$ respectively. The work done to bring the charge from $C$ to $A$ is

In a hydrogen atom, the electron and proton are bound at a distance of about $0.53\; \mathring A:$

$(a)$ Estimate the potential energy of the system in $eV$, taking the zero of the potential energy at infinite separation of the electron from proton.

$(b)$ What is the minimum work required to free the electron, given that its kinetic energy in the orbit is half the magnitude of potential energy obtained in $(a)?$

$(c)$ What are the answers to $(a)$ and $(b)$ above if the zero of potential energy is taken at $1.06\;\mathring A$ separation?

A particle $A$ has charge $+q$ and particle $B$ has charge $+4 q$ with each of them having the same mass $m$. When allowed to fall from rest through the same electric potential difference, the ratio of their speeds $\frac{V_A}{V_B}$ will become

In Millikan's experiment, an oil drop having charge $q$ gets stationary on applying a potential difference $V$ in between two plates separated by a distance $d$. The weight of the drop is