ADDITIONAL EXERCISES

A charge of $8 \mathrm{mC}$ is placed at the origin. Calculate the work done in taking a small charge of $-2\times {10}^{-9} \mathrm{C}$ from $P$ $\left(0, 0, 3 \mathrm{cm}\right)$ to a point $Q$ $\left(0, 4 \mathrm{cm}, 0\right)$ via point $R$$\left(0, 6 \mathrm{cm}, 9 \mathrm{cm}\right)$.

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, $\frac{1}{4\mathrm{\pi }{\in }_0} = 9\times {10}^9 \mathrm{N} {\mathrm{m}}^2 {\mathrm{C}}^{-2}$

Describe schematically the equipotential surfaces corresponding to a uniform grid consisting of long equally spaced parallel charged wires in a plane.

A small sphere of radius ${\mathrm{r}}_1$ and charge ${\mathrm{q}}_1$ is enclosed by a spherical shell of radius ${\mathrm{r}}_2$ and charge ${\mathrm{q}}_2.$ Show that if ${\mathrm{q}}_1$ is positive, charge will necessarily flow from the sphere to the shell (when the two are connected by a wire) no matter what the charge ${\mathrm{q}}_2$ on the shell is.

The top of the atmosphere is at about $400 \mathrm{k}\mathrm{V}$ with respect to the surface of the earth, corresponding to an electric field that decreases with altitude. Near the surface of the earth, the field is about $100 \mathrm{V}{\mathrm{m}}^{–1}.$ Why then do we not get an electric shock as we step out of our house into the open? (Assume the house to be a steel cage so there is no field inside!)

A man fixes outside his house one evening a two meter high insulating slab carrying on its top a large aluminium sheet of area $1 {\mathrm{m}}^2.$ Will he get an electric shock if he touches the metal sheet next morning?

The discharging current in the atmosphere due to the small conductivity of air is known to be $1800 \mathrm{A}$ on an average over the globe. Why then does the atmosphere not discharge itself completely in due course and become electrically neutral? In other words, what keeps the atmosphere charged?

What are the forms of energy into which the electrical energy of the atmosphere is dissipated during a lightning?