Two tiny spheres carrying charges $1.5 \mathrm{\mu C}$ and $2.5 \mathrm{\mu C}$ are located $30 \mathrm{cm}$ apart. Find the potential and electric field at the midpoint of line joining the two charges. Take, $\frac{1}{4\mathrm{\pi }{\in }_0} = 9\times {10}^9 \mathrm{N} {\mathrm{m}}^2 {\mathrm{C}}^{-2}$

Two tiny spheres carrying charges $1.5 \mathrm{\mu C}$ and $2.5 \mathrm{\mu C}$ are located $30 \mathrm{cm}$ apart. Find the potential and electric field at a point $10 \mathrm{cm}$ from this midpoint in a plane normal to the line joining the two charges and passing through the midpoint.

Show that the normal component of electrostatic field has a discontinuity from one side of a charged surface to another given by $\left({\overrightarrow{E}}_2-{\overrightarrow{E}}_1\right)\cdot \hat{n}=\frac{\sigma }{{\epsilon }_0}$ where $\widehat{n}$ is a unit vector normal to the surface at a point and $\sigma$ is the surface charge density at that point (The direction of $\hat{n}$ is from side $1$ to side $2$). Hence, show that just outside a conductor, the electric field is $\frac{\sigma \widehat{n}}{{\epsilon }_0}$.

In a hydrogen atom, the electron and proton are bound at a distance of about $0.53 {\mathrm{A}}^{°}$. Estimate the potential energy of the system in $\mathrm{eV}$, taking the zero of the potential energy at infinite separation of the electron from proton. What is the value if the zero potential energy is taken at $1.06 {\mathrm{A}}^{°}$ separation?