Q. No.| 1. | \(9 \times 10^{-3}~\text{J}\) | 2. | \(9 \times 10^{-3}~\text{eV}\) |
| 3. | \(2~\text{eV/m}\) | 4. | zero |
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:
| 1. | \(-\frac{q}{2} \) | 2. | \(-q\) |
| 3. | \(+q\) | 4. | \(\text{zero}\) |
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:
| 1. | \(3\times 10^{-4}~\text{J}\) | 2. | \(-3\times 10^{-4}~\text{J}\) |
| 3. | \(9\times 10^{-6}~\text{J}\) | 4. | \(-9\times 10^{-6}~\text{J}\) |
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:
| 1. | \(8q_2\) | 2. | \(8q_1\) |
| 3 | \(6q_2\) | 4. | \(6q_1\) |
(Taking the zero of the potential energy at an infinite separation of the electron from the proton.)
| 1. | \(-23.1\) eV | 2. | \(27.0\) eV |
| 3. | \(-27.2\) eV | 4. | \(23.7\) eV |
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?
| 1. | \(\frac{Z e^2}{2 \pi \varepsilon_0 m v^2} \) | 2. | \(\frac{Z_e}{4 \pi \varepsilon_0 m v^2} \) |
| 3. | \(\frac{Z e^2}{8 \pi \varepsilon_0 m v^2} \) | 4. | \(\frac{Z_e}{8 \pi \varepsilon_0 m v^2}\) |
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:
| 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)
| 1. | \(87.5\) | 2. | \(112.5\) |
| 3. | \(150\) | 4. | \(250\) |
Figure shows a ball having a charge \(q\) fixed at a point . Two identical balls having charges \(+q\) and \(–q\) and mass \(‘m’\) each are attached to the ends of a light rod of length \(2 a\)
| 1. | \(\frac{\sqrt{2}q}{3 \pi \varepsilon_0 {ma}^3} \) | 2. | \(\frac{q}{\sqrt{3 \pi \varepsilon_0 {ma}^3 }}\) |
| 3. | \(\frac{q}{\sqrt{6 \pi \varepsilon_0 {ma}^3 }} \) | 4. | \(\frac{\sqrt{2} q}{4 \pi \varepsilon_0 m a^3} \) |
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