The dimensional formula of $k$ (Coulomb's constant) is . . . . . . .
(Take $I$ as the dimension of current.)

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: $\frac{1}{4\pi\varepsilon_0} = 9 \times 10^9\, N\cdot m^2/C^2$)

Two electrons are moving towards each other,each with a velocity of $10^6 \, m/s$. What will be the closest distance of approach between them in $m$?

$5$ charges each of magnitude $10^{-5} \,C$ and mass $1 \,kg$ are placed (fixed) symmetrically about a movable central charge of magnitude $5 \times 10^{-5} \,C$ and mass $0.5 \,kg$ as shown in the figure. The charge at $P_1$ is removed. The acceleration of the central charge is [Given,$O P_1=O P_2=O P_3=O P_4=O P_5=1 \,m, \frac{1}{4 \pi \varepsilon_0}=9 \times 10^9 \,N \cdot m^2/C^2$]

$N$ point charges are distributed into two groups and separated by a fixed distance. Then the ratio of maximum to minimum forces between the two groups is ($N$ is even and greater than $2$).

Three point charges $+q$,$+2q$,and $+4q$ are placed along a straight line such that the charge $+2q$ is equidistant from the other two charges. The ratio of the net electrostatic force on charges $+q$ and $+4q$ is