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?

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.