(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) |
(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. |
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. \(\frac{1}{4 π\varepsilon_{0}} \frac{8 p_{1} p_{2}}{x^{4}}\)
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:
\(\left(\dfrac{1}{4 \pi \varepsilon_0}=9 \times 10^9~ \text{Nm}^2 \text{C}^{-2}\right)\)
1. | \( 10^{24} ~\text{m/s}^2\) | 2 | \( 10^{23} ~\text{m/s}^2\) |
3. | \( 10^{22}~\text{m/s}^2\) | 4. | \( 10^{25} ~\text{m/s}^2\) |
The figure shows electric field lines in which an electric dipole \(p\) is placed as shown. Which of the following statements is correct?
1. | The dipole will not experience any force. |
2. | The dipole will experience a force towards the right. |
3. | The dipole will experience a force towards the left. |
4. | The dipole will experience a force upwards. |
The electric field at a distance \(\frac{3R}{2}\) from the centre of a charged conducting spherical shell of radius \(R\) is \(E\). The electric field at a distance \(\frac{R}{2}\) from the centre of the sphere is:
1. \(E\)
2. \(\frac{E}{2}\)
3. \(\frac{E}{3}\)
4. zero
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. |