B M Sharma Solutions for Chapter: Coulomb's Law and Electric Field, Exercise 2: Concept Application Exercise

Two particles $A$ and $B$ having charges $8\times {10}^{-6 }\mathrm{C}$ and $-2\times {10}^{-6} \mathrm{C}$, respectively, are held fixed with a separation of $20 \mathrm{c}\mathrm{m}$. Where should a third charged particle be placed so that it does not experience net electric force?

A particle of mass $m$ carrying a charge $-q_1$ starts moving around a fixed charge $+q_2$ along a circular path of radius $r$. Find the time period of revolution $T$ of charge $-q_1$.

Two identical conducting small spheres are placed with their centres $0.3 \mathrm{m}$ apart. One is given a charge of $12.0 \mathrm{nC}$ and the other a charge of $-18.0 \mathrm{nC}$.

(a) Find the electric force exerted by one sphere on the other?

(b) If the spheres are connected by a conducting wire, find the electric force between the two after they attain equilibrium.

Four equal point charges, each of magnitude $+Q$, are to be placed in equilibrium at the corners of a square. What should be the magnitude and sign of the point charge that should be placed at the centre of the square to do this job?

Two point electric charges of values $q$ and $2q$ are kept at a distance $d$ apart from each other in air. A third charge $-Q$ is to be kept along the same line in such a way that the net force acting on $q$ and $2q$ is zero. Find the location of the third charge from charge $q$.

Two identical particles are charged and held at a distance of $1 \mathrm{m}$ from each other. They are found to be attracting each other with a force of $0.027 \mathrm{N}$. Now, they are connected by a conducting wire so that charge flows between them. When the charge flow stops, they are found to be repelling each other with a force of $0.009 \mathrm{N}$. Find the initial charge on each particle.

A copper atom consists of a copper nucleus surrounded by $29$ electrons. The atomic weight of copper is $63.5 \mathrm{g} {\mathrm{mol}}^{-1}$. Let us now take pieces of copper each weighing $10 \mathrm{g}$. Let one electron from one piece be transferred to another for every $1000$ atoms in a piece.

(a) Find the magnitude of the charge appearing on each piece.

(b) What will be the Coulomb force between the two pieces after the transfer of electrons if they are $10 \mathrm{cm}$ apart? (Avogadro’s number is $6\times {10}^{23} \mathrm{m}\mathrm{o}{\mathrm{l}}^{-1}$).

Two identical small equally charged conducting balls are suspended from long threads secured at one point. The charges and masses of the balls are such that they are in equilibrium when the distance between them is $a$ (the length of thread $L\gg a$). Then one of the balls is discharged. What will be the distance $b\left(b\ll L\right)$ between the balls when equilibrium is restored?