Q. No.What is the potential energy of two equal positive point charges of \(1~ \mu \text{C}\) each held \(1\) m apart in the air?
| 1. | \(9 \times 10^{-3}~\text{J}\) | 2. | \(9 \times 10^{-3}~\text{eV}\) |
| 3. | \(2~\text{eV/m}\) | 4. | zero |
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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. | \(\text{zero}\) |
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A charge \(q_1=5 \times 10^{-8} \mathrm{~C}\) is kept at 3 cm from a charge \(q_2=-2 \times 10^{-8} \mathrm{~C}\). The potential energy of the system relative to the potential energy at infinite separation is:
1. 3 x J
2. –3 x J
3. 9 x J
4. –9 x J
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In a hydrogen atom, the electron and proton are bound at a distance of about 0.53 Å. The potential energy of the system in eV is:
(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. | \(\frac{Z_e}{8 \pi \varepsilon_0 m v^2}\) |
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Two charges q1 and q2 are placed 30 cm apart, as shown in the figure. A third charge q3 is moved along the arc of a circle of radius 40 cm from C to D. The change in the potential energy of the system is , where k is:
| 1. | 8q2 | 2. | 8q1 |
| 3 | 6q2 | 4. | 6q1 |
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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 |
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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.
3.
4.
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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. | \(\frac{\sqrt{2} \mathrm{q}}{3 \pi \epsilon_0 \mathrm{ma}^3} \) | 2. | \(\frac{\mathrm{q}}{\sqrt{3 \pi \epsilon_0 \mathrm{ma}^3 }}\) |
| 3. | \(\frac{\mathrm{q}}{\sqrt{6 \pi \epsilon_0 \mathrm{ma}^3 }} \) | 4. | \(\frac{\sqrt{2} q}{4 \pi \epsilon_0 m a^3} \) |
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Three charges \(-Q\), \(q\), and \(-2Q\) are placed along a line as shown in the figure. The system of charges will have a positive potential energy configuration when q is placed at midpoint of line joining \(-Q\) and \(-2Q\), if:
| 1. | \(q>{Q \over 3}\) | 2. | \(q<{Q \over 3}\) |
| 3. | \(q>{-Q \over 3}\) | 4. | \(q<{-Q \over 3}\) |
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