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 point-like charges $a$ and $b$ whose strengths are equal in absolute value are positioned at a certain distance from each other. Assuming the field strength is positive in the direction coinciding with the positive direction of the $r$ axis, determine the signs of the charges for each distribution of the field strength between charges shown in figure.
   

Two points charges $\pm q$ are placed on the axis at $x=-a$ and $x=+a$, as shown in the figure.

(a) Plot the variation of $E$ along the $x$-axis.

(b) Plot the variation of $E$ along the $y$-axis.

Three small spheres $x\text{,} y$ and $z$ carry charges of equal magnitudes and with signs shown in figure. They are placed at the vertices of an isosceles triangle with the distance between $x$ and $z$. The spheres $y$ and $z$ are held in place but sphere $x$ is free to move on a frictionless surface.

(a) What is the direction of the electric force on sphere $x$ at the point shown in the figure?

(b) Which path is sphere $x$ likely to take when released?