NCERT Solutions for Chapter: Electric Charges and Fields, Exercise 2: ADDITIONAL EXERCISES

A conductor $A$ with a cavity as shown in figure is given a charge $Q$. Show that the entire charge must appear on the outer surface of the conductor.

A conductor $\mathrm{A}$ with cavity as shown in the figure is given a charge $Q$. Another conductor $\mathrm{B}$ with charge $q$ is inserted into the cavity keeping $\mathrm{B}$ insulated from $\mathrm{A}$. Show that the total charge on outside the surface of $\mathrm{A}$ is $Q+q$.

A sensitive instrument is to be shielded from the strong electrostatic fields in its environment. Suggest a possible way.

A hollow charged conductor has a tiny hole cut into its surface. Show that the electric field in the hole is ( $\sigma /2{ϵ}_0$) $\widehat{n}$, where $\widehat{n}$ is the unit vector in the outward normal direction, and $\sigma$ is the surface charge density near the hole.

Obtain the formula for the electric field due to a long thin wire of uniform linear charge density $E$ without using Gauss’s law. [Hint: Use Coulomb’s law directly and evaluate the necessary integral.]

It is now believed that protons and neutrons (which constitute nuclei of ordinary matter) are themselves built out of more elementary units called quarks. A proton and a neutron consist of three quarks each. Two types of quarks, the so called ‘up’ quark (denoted by $u$) of charge $+\mathrm{}(2/3)\mathrm{}\mathrm{e},$ and the ‘down’ quark (denoted by $d$) of charge $(–1/3)\mathrm{}\mathrm{e},$ together with electrons build up ordinary matter. (Quarks of other types have also been found which give rise to different unusual varieties of matter.) Suggest a possible quark composition of a proton and neutron.

Consider an arbitrary electrostatic field configuration. A small test charge is placed at a null point (i.e., where $\mathrm{E}=0$) of the configuration. Show that the equilibrium of the test charge is necessarily unstable. Verify this result for the simple configuration of two charges of the same magnitude and sign placed a certain distance apart.

A particle of mass $m$ and charge $(–q)$ enters the region between the two charged plates initially moving along $\mathrm{x}$-axis with speed ${\upsilon }_x$.The length of plate is $L$ and an uniform electric field $E$ is maintained between the plates.
(a) Show that the vertical deflection of the particle at the far edge of the plate is $qE{L}^2/\left(2m{\upsilon }_x^2\right).$ Compare this motion with motion of a projectile in gravitational field.

(b) Suppose that the particle is an electron projected with velocity ${\mathrm{\upsilon }}_{\mathrm{x}}=2.0\times {10}^6 {\mathrm{ms}}^{–1}$. If $E$ between the plates separated by $0.5 \mathrm{cm}$ is $9.1\times {10}^2 \mathrm{N}/\mathrm{C},$ where will the electron strike the upper plate? $(\left|e\right|=1.6\times {10}^{–19}\mathrm{C}, m_e=9.1\times {10}^{–31}\mathrm{k}\mathrm{g}.)$