$5$ 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 given below. The charge at $P_1$ is removed. The acceleration of the central charge is [Given, $\left.O P_1=O P_2=O P_3=O P_4=O P_5=1 m , \frac{1}{4 \pi \varepsilon_0}=9 \times 10^9\right]$

$12$ positive charges of magnitude $q$ are placed on a circle of radius $R$ in a manner that they are equally spaced. A charge $Q$ is placed at the centre, if one of the charges $q$ is removed, then the force on $Q$ is

A charge $q$ is placed at the centre of the line joining two equal charges $Q$. The system of the three charges will be in equilibrium, if $q$ is equal to

Two small spherical balls each carrying a charge $Q = 10\,\mu C$ ($10\, micro-coulomb$) are suspended by two insulating threads of equal lengths $3\, m$ each, from a point fixed in the ceiling. It is found that in equilibrium threads are separated by an angle $120^o$ between them, as shown in the figure. What is the tension in the threads (Given : $\frac{1}{{\left( {4\pi {\varepsilon _0}} \right)}} = 9 \times {10^9}\,Nm/{C^2}$)

Positive charge $Q$ is distributed uniformly over a circular ring of radius $R$. A point particle having a mass $(m)$ and a negative charge $-q$ is placed on its axis at a distance $x$ from the centre. Assuming $x < R,$ find the time period of oscillation of the particle, if it is released from there [neglect gravity].

Write Coulomb’s law and explain its scalar form.