Q. No.A total charge \(Q\) is broken in two parts \(Q_1\) and \(Q_2\) and they are placed at a distance \(R\) from each other. The maximum force of repulsion between them will occur, when:
| 1. | \(Q_2=\frac{Q}{R}, Q_1=Q-\frac{Q}{R}\) |
| 2. | \(Q_2=\frac{Q}{4}, Q_1=Q-\frac{2 Q}{3}\) |
| 3. | \(Q_2=\frac{Q}{4}, Q_1=\frac{3 Q}{4}\) |
| 4. | \(Q_1=\frac{Q}{2}, Q_2=\frac{Q}{2}\) |
Two charges \(+2\) C and \(+6\) C are repelling each other with a force of \(12\) N. If each charge is given \(-2\) C of charge, then the value of the force will be:
| 1. | \(4\) N (attractive) | 2. | \(4\) N (repulsive) |
| 3. | \(8\) N (repulsive) | 4. | zero |
| 1. | \(4~\text{cm}\) from \(2~\mu\text{C}.\) |
| 2. | \(2~\text{cm}\) from \(2~\mu\text{C}.\) |
| 3. | \(2~\text{cm}\) from \(8~\mu\text{C}.\) |
| 4. | \(3~\text{cm}\) from \(8~\mu\text{C}.\) |
Two positive ions, each carrying a charge \(q\), are separated by a distance \(d\). If \(F\) is the force of repulsion between the ions, the number of electrons missing from each ion will be:
(\(e\) is the charge on an electron)
| 1. | \(\frac{4 \pi \varepsilon_{0} F d^{2}}{e^{2}}\) | 2. | \(\sqrt{\frac{4 \pi \varepsilon_{0} F e^{2}}{d^{2}}}\) |
| 3. | \(\sqrt{\frac{4 \pi \varepsilon_{0} F d^{2}}{e^{2}}}\) | 4. | \(\frac{4 \pi \varepsilon_{0} F d^{2}}{q^{2}}\) |
The acceleration of an electron due to the mutual attraction between the electron and a proton when they are \(1.6~\mathring{A}\) apart is:
\(\left(\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9~ \text{Nm}^2 \text{C}^{-2}\right)\)
| 1. | \( 10^{24} ~\text{m/s}^2\) | 2 | \( 10^{23} ~\text{m/s}^2\) |
| 3. | \( 10^{22}~\text{m/s}^2\) | 4. | \( 10^{25} ~\text{m/s}^2\) |
| 1. | \(\frac{4F}{3}\) | 2. | \(F\) |
| 3. | \(\frac{9F}{16}\) | 4. | \(\frac{16F}{9}\) |
| 1. | Newton metre2 / Coulomb2 |
| 2. | Coulomb2 /Newton metre2 |
| 3. | Coulomb2/ (Newton metre)2 |
| 4. | Coulomb/Newton metre |
Two small spheres each having the charge \(+Q\) are suspended by insulating threads of length \(L\) from a hook. If this arrangement is taken in space where there is no gravitational effect, then the angle between the two suspensions and the tension in each will be:
1. \(180^\circ,\) \(\frac{1}{4 \pi \epsilon_{0}} \frac{Q^{2}}{(2 L )^{2}}\)
2. \(90^\circ,\) \(\frac{1}{4 \pi \epsilon_{0}} \frac{Q^{2}}{(L )^{2}}\)
3. \(180^\circ,\) \(\frac{1}{4 \pi \epsilon_{0}} \frac{Q^{2}}{2 L ^{2}}\)
4. \(180^\circ,\) \(\frac{1}{4 \pi \epsilon_{0}} \frac{Q^{2}}{ L ^{2}}\)
Four charges are arranged at the corners of a square \(ABCD\) as shown in the figure. The force on a positive charge kept at the center of the square is:
| 1. | zero |
| 2. | along diagonal \(AC\) |
| 3. | along diagonal \(BD\) |
| 4. | perpendicular to the side \(AB\) |
| 1. | \(\dfrac {F}{4}\) | 2. | \(12F\) |
| 3. | \(6F\) | 4. | \(3F\) |
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