In a right-angled triangle $ABC$,$AB = 3 \ cm$,$BC = 4 \ cm$,and $\angle ABC = \frac{\pi}{2}$. Charges of $+15 \ e.s.u.$,$+12 \ e.s.u.$,and $-20 \ e.s.u.$ are placed at $A$,$B$,and $C$ respectively. What is the net force on the charge at $B$ in $dynes$?

The charges on two spheres are $+7\,\mu C$ and $-5\,\mu C$ respectively. They experience a force $F$. If each of them is given an additional charge of $-2\,\mu C$,the new force of attraction will be

Two charges $q$ and $-3q$ are placed fixed on the $x$-axis separated by a distance $d$. Where should a third charge $2q$ be placed such that it will not experience any force?

Two small spheres of masses $M_1$ and $M_2$ are suspended by weightless insulating threads of lengths $L_1$ and $L_2$ respectively. The charges on the spheres are $Q_1$ and $Q_2$ respectively. The spheres are suspended such that they lie in a horizontal line and the threads make angles $\theta_1$ and $\theta_2$ with the vertical as shown in the figure. Which of the following conditions is necessary for $\theta_1 = \theta_2$?

Two point charges of $+2\,\mu C$ and $+6\,\mu C$ repel each other with a force of $12\,N$. If each is given an additional charge of $-4\,\mu C$,then the force will become:

Two point charges $+e$ and $+4e$ are kept at a distance $d$ units apart. $A$ third point charge $+q$ is placed between the two charges at a distance $x$ units from charge $+e$ so as to be in equilibrium. The value of $x$ is: