A particle of mass \(m\) carrying charge \(-q_1\) is moving around a charge \(+q_2\) along a circular path of radius \(r\). The period of revolution of the charge \(-q_1\) is:
1. \(\sqrt{\frac{16\pi^{3} \varepsilon_{0} mr^{3}}{q_{1} q_{2}}}\)
2. \(\sqrt{\frac{8\pi^{3} \varepsilon_{0} mr^{3}}{q_{1} q_{2}}}\)
3. \(\sqrt{\frac{q_{1} q_{2}}{16 \pi^{3} \varepsilon_{0} mr^{3}}}\)
4. zero
1. | Only \(-q\) is in stable equilibrium. |
2. | None of the charges are in equilibrium. |
3. | All the charges are in unstable equilibrium. |
4. | All the charges are in stable equilibrium. |
Two point dipoles of dipole moment \(\vec{p}_{1}\) and \(\vec{p}_{2}\) are at a distance \(x\) from each other and \(\vec{p}_{1} \left|\right| \vec{p}_{2}\). The force between the dipole is:
1. \(\frac{1}{4 π\varepsilon_{0}} \frac{4 p_{1} p_{2}}{x^{4}}\)
2. \(\frac{1}{4 π\varepsilon_{0}} \frac{3 p_{1} p_{2}}{x^{3}}\)
3. \(\frac{1}{4π\varepsilon_{0}} \frac{6 p_{1} p_{2}}{x^{4}}\)
4. \(\frac{1}{4 π\varepsilon_{0}} \frac{8 p_{1} p_{2}}{x^{4}}\)
A hollow metal sphere of radius \(R\) is uniformly charged. The electric field due to the sphere at a distance \(r\) from the centre:
1. | decreases as \(r\) increases for \(r<R\) and for \(r>R\). |
2. | increases as \(r\) increases for \(r<R\) and for \(r>R\). |
3. | is zero as \(r\) increases for \(r<R\), decreases as \(r\) increases for \(r>R\). |
4. | is zero as \(r\) increases for \(r<R\), increases as \(r\) increases for \(r>R\). |
1. | \(\dfrac{Q+q}{4 \pi r_{2}^{2}}\) | 2. | \(\dfrac{q}{4 \pi r_{1}^{2}}\) |
3. | \(\dfrac{-Q+q}{4 \pi r_{2}^{2}}\) | 4. | \(\dfrac{-q}{4 \pi r_{1}^{2}}\) |
1. | \(10^{-2}~\text{N-m}\) |
2. | \(0\) |
3. | \(10^{-1}~\text{N-m}\) |
4. | \(0.01~\text{N-m}\) |
A polythene piece rubbed with wool is found to have a negative charge of \(3 \times10^{-7}~\text{C}\). Transfer of mass from wool to polythene is:
1. \(0.7\times10^{-18}~\text{kg}\)
2. \(1.7\times10^{-17}~\text{kg}\)
3. \(0.7\times10^{-17}~\text{kg}\)
4. \(1.7\times10^{-18}~\text{kg}\)
(a) | on any surface. |
(b) | if the charge is outside the surface. |
(c) | could not be defined. |
(d) | if charges of magnitude \(q\) were inside the surface. |
(a) | the electric field is necessarily zero. |
(b) | the electric field is due to the dipole moment of the charge distribution only. |
(c) | the dominant electric field is \(\propto \dfrac 1 {r^3}\), for large \(r\), where \(r\) is the distance from the origin in this region. |
(d) | the work done to move a charged particle along a closed path, away from the region, will be zero. |
Which of the above statements are true?
1. (b) and (d)
2. (a) and (c)
3. (b) and (c)
4. (c) and (d)
Refer to the arrangement of charges in the figure and a Gaussian surface of radius \(R\) with \(Q\) at the centre. Then:
(a) | total flux through the surface of the sphere is \(\dfrac{-Q}{\varepsilon_0}\). |
(b) | field on the surface of the sphere is \(\dfrac{-Q}{4\pi \varepsilon_0 R^2}.\) |
(c) | flux through the surface of the sphere due to \(5Q\) is zero. |
(d) | field on the surface of the sphere due to \(-2Q\) is the same everywhere. |
Choose the correct statement(s):
1. | (a) and (d) | 2. | (a) and (c) |
3. | (b) and (d) | 4. | (c) and (d) |