Two charges of $+2\,C$ and $+6\,C$ repel each other with a force of $12\,N$. If each charge is given an additional charge of $-2\,C$,what will be the new force between them?

Two small spherical balls,each carrying a charge $Q = 10\,\mu C$ ($10$ micro-coulomb),are suspended by two insulating threads of equal lengths $1\,m$ each,from a point fixed in the ceiling. It is found that in equilibrium,the threads are separated by an angle of $60^o$ between them,as shown in the figure. What is the tension in the threads in $N$? (Given: $\frac{1}{4\pi \varepsilon_0} = 9 \times 10^9\,Nm^2/C^2$)

The force between two point charges $A$ and $B$ is $F$. If $75\%$ of the charge of $A$ is transferred to $B$,then the new force between $A$ and $B$ is:

$A$ particle of mass $M$ and charge $q$ is placed at the midpoint between two fixed charges each of magnitude $Q$, separated by a distance $2d$. The system is collinear as shown in the figure. If the particle is displaced by a small distance $x$ $(x \ll d)$ along the line joining the two charges and released, it will oscillate about the mean position with a time period $T$. ($\varepsilon_{0}$ is the permittivity of free space)

State Coulomb's law and explain its scalar form.

Two small balls,each having mass $m$ and charge $q$,are suspended from a common point by insulating strings of length $L$ as shown in the figure. Assuming $\theta$ is very small such that $\tan \theta \approx \sin \theta$,find the value of $x$ at equilibrium.