S L Arora Solutions for Chapter: Electric Charges and Field, Exercise 5: GUIDELINES TO NCERT EXERCISES

What is the force between two small charged sphere having charges of $2\times {10}^{-7} \mathrm{C}$ and $3\times {10}^{-7} \mathrm{C}$ placed $30 \mathrm{cm}$ apart in air? ($k = 9\times {10}^9 {\mathrm{Nm}}^2{\mathrm{C}}^{-2}$)

The electrostatic force on a small sphere of charge $0.4 \mathrm{\mu }\mathrm{C}$ due to another small sphere of charge $–0.8 \mathrm{\mu }\mathrm{C}$ in the air is $0.2 \mathrm{N} .$ What is the distance between the two spheres? ($k = 9\times {10}^9 {\mathrm{Nm}}^2{\mathrm{C}}^{-2}$)

The electrostatic force on a small sphere of charge $0.4 \mathrm{\mu }\mathrm{C}$ due to another small sphere of charge $–0.8 \mathrm{\mu }\mathrm{C}$ in the air is $0.2 \mathrm{N}.$
What is the force on the second sphere due to the first?

Four-point charges ${\mathrm{q}}_{\mathrm{A}}=2 \mathrm{\mu }\mathrm{C}, {\mathrm{q}}_{\mathrm{B}}=–5 \mathrm{\mu }\mathrm{C}, {\mathrm{q}}_{\mathrm{C}}=2 \mathrm{\mu }\mathrm{C},\mathrm{and} {\mathrm{q}}_{\mathrm{D}}=–5 \mathrm{\mu }\mathrm{C}$ are located at the corners of a square $\mathrm{ABCD}$ of side $10 \mathrm{cm}$. What is the force on a charge of $1 \mathrm{\mu }\mathrm{C}$ placed at the center of the square?

Two point charges $q_A=3 \mathrm{\mu }\mathrm{C}$ and  $q_{B }=-3 \mathrm{\mu C}$ are located $20 \mathrm{cm}$ apart in vacuum. What is the electric field at the midpoint $\mathrm{O}$ of the line $\mathrm{AB}$ joining the two charges? If a negative test charge of magnitude $1.5\times {10}^{-9} \mathrm{C}$ is placed at this point, what is the force experienced by the test charge? Take, $\frac{1}{4\pi {\in }_0}=9\times {10}^9 {\mathrm{Nm}}^2{\mathrm{C}}^{-2}$

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 $Q+q$.

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? $(\left|e\right|=1.6\times {10}^{–19}\mathrm{C}, m_e=9.1\times {10}^{–31}\mathrm{k}\mathrm{g}.)$