Two point charges $q_1$ and $q_2$ are $l$ distance apart. If one of the charges is doubled and the distance between them is halved, the magnitude of the force becomes $n$ times, where $n$ is:

$A$ charge $Q$ is divided into two parts $Q_1$ and $Q_2$. For a given distance $R$,the force between them is maximum when:

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 small spherical balls each carrying a charge $Q = 10\,\mu C$ are suspended by two insulating threads of equal lengths $L = 3\, m$ each,from a point fixed in the ceiling. It is found that in equilibrium,the threads are separated by an angle of $120^{\circ}$ between them,as shown in the figure. What is the tension in the threads? (Given: $\frac{1}{4\pi\varepsilon_0} = 9 \times 10^9\, N\cdot m^2/C^2$)

Three charges $+Q, q, +Q$ are placed respectively at distances $0, \frac{d}{2},$ and $d$ from the origin on the $x$-axis. If the net force experienced by the charge $+Q$ placed at $x = 0$ is zero,then the value of $q$ is:

An infinite number of point charges,each carrying $1 \,\mu C$ charge,are placed along the y-axis at $y=1 \,m, 2 \,m, 4 \,m, 8 \,m, \ldots$. The total force on a $1 \,C$ point charge,placed at the origin,is $x \times 10^{3} \,N$. The value of $x$,to the nearest integer,is .........
[Take $\frac{1}{4 \pi \epsilon_{0}}=9 \times 10^{9} \,N m^{2}/C^{2}$]