Three charges $Q$, $+q$ and $+q$ are placed at the vertices of an equilateral triangle of side $l$ as shown in the figure. If the net electrostatic energy of the system is zero, then $Q$ is equal to:

A charge $q_1=5 \times 10^{-8} ~\text{C}$ is kept at $3$ cm from a charge $q_2=-2 \times 10^{-8} ~\text{C}$. The potential energy of the system relative to the potential energy at infinite separation is:

Two charges $q_1$ and $q_2$ are placed $30~\text{cm}$ apart, as shown in the figure. A third charge $q_3$ is moved along the arc of a circle of radius $40~\text{cm}$ from $C$ to $D.$ The change in the potential energy of the system is $\dfrac{q_{3}}{4 \pi \varepsilon_{0}} k,$ where $k$ is:

An elementary particle of mass $m$ and charge $+e$ is projected with velocity $v$ at a much more massive particle of charge $Ze$, where $Z>0$. What is the closest possible approach of the incident particle?

When a particle with charge $+q$ is thrown with an initial velocity $v$ towards another stationary change $+Q,$ it is repelled back after reaching the nearest distance $r$ from $+Q.$ The closest distance that it can reach if it is thrown with an initial velocity $2v,$ is:

Four equal charges $Q$ are placed at the four corners of a square of each side $a$. Work done in removing a charge $-Q$ from its centre to infinity is:
1. $0$
2. $\frac{\sqrt{2} Q^{2}}{4 \pi \varepsilon_{0} a}$
3. $\frac{\sqrt{2} Q^{2}}{\pi \varepsilon_{0} a}$
4. $\frac{Q^{2}}{2 \pi \varepsilon_{0} a}$

A charge of $10$ e.s.u. is placed at a distance of $2$ cm from a charge of $40$ e.s.u. and $4$ cm from another charge of $20$ e.s.u. The potential energy of the charge $10$ e.s.u. is: (in ergs) 

Figure shows a ball having a charge $q$ fixed at a point $\mathrm{A}$. Two identical balls having charges $+q$ and $–q$ and mass $‘m’$ each are attached to the ends of a light rod of length $2 a$. The rod is free to rotate about a fixed axis perpendicular to the plane of the paper and passing through the mid-point of the rod. The system is released from the situation as shown in the figure. The angular velocity of the rod when the rod becomes horizontal will be: