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?

A positively charged particle \(+q\) is projected with speed vvv toward a fixed charge \(+Q,\) and rebounds after reaching a minimum distance \(r.\) What will be the new closest distance of approach if its initial velocity is doubled to \(2v\text{?}\)
1. \(\dfrac{r}{4}\)

2. \(\dfrac{r}{2}\)

3. \(\dfrac{r}{16}\)

4. \(\dfrac{r}{8}\)

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 $\mathrm{}$\(2 a\). 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: