When two spheres having $4 Q$ and $-2 Q$ charge are placed at a certain distance,the force acting between them is $F$. Now they are connected by a conducting wire and again separated from each other. Now they are kept at a distance half of the previous one. The force acting between them is . . . . . . .

In a regular polygon of $n$ sides,each corner is at a distance $r$ from the centre. Identical charges are placed at $(n - 1)$ corners. At the centre,the intensity is $E$ and the potential is $V$. The ratio $V/E$ has magnitude.

Six charges,three positive and three negative of equal magnitude,are placed at the corners of a regular hexagon such that the electric field at the center $O$ is double the electric field obtained when only a charge of the same magnitude is placed at $R$. What are the charges at $P, Q, R, S, T,$ and $U$ respectively?

Two fixed charges $+4\,Q$ and $-Q$ are located at $A$ and $B$ respectively,with the distance $AB = 3\,m$.

Two charged identical metal spheres $A$ and $B$ repel each other with a force of $3 \times 10^{-5} \,N$. Another identical uncharged sphere $C$ is touched with sphere $A$ and then it is placed mid-way between $A$ and $B$. Then, the magnitude of net force on $C$ is

Answer carefully:
$(a)$ Two large conducting spheres carrying charges $Q_{1}$ and $Q_{2}$ are brought close to each other. Is the magnitude of electrostatic force between them exactly given by $Q_{1} Q_{2} / 4 \pi \varepsilon_{0} r^{2}$,where $r$ is the distance between their centres?
$(b)$ If Coulomb's law involved $1/r^{3}$ dependence (instead of $1/r^{2}$),would Gauss's law be still true?
$(c)$ $A$ small test charge is released at rest at a point in an electrostatic field configuration. Will it travel along the field line passing through that point?
$(d)$ What is the work done by the field of a nucleus in a complete circular orbit of the electron? What if the orbit is elliptical?
$(e)$ We know that electric field is discontinuous across the surface of a charged conductor. Is electric potential also discontinuous there?
$(f)$ What meaning would you give to the capacitance of a single conductor?
$(g)$ Guess a possible reason why water has a much greater dielectric constant $(=80)$ than,say,mica $(=6)$?