(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. |
1. | (a) and (d) | 2. | (a) and (c) |
3. | (b) and (d) | 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) |
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. |
A charge \(q\) is placed in a uniform electric field \(E.\) If it is released, then the kinetic energy of the charge after travelling distance \(y\) will be:
1. | \(qEy\) | 2. | \(2qEy\) |
3. | 4. |
The electric field at the equator of a dipole is \(E.\) If the strength of the dipole and distance are now doubled, then the electric field will be:
1. | \(E/2\) | 2. | \(E/8\) |
3. | \(E/4\) | 4. | \(E\) |
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 \(r>R\). |
In Millikan oil drop experiment, a charged drop falls with a terminal velocity \(v\). If an electric field \(E\) is applied vertically upwards it moves with terminal velocity \(2v\) in upward direction. If electric field reduces to \(\frac{E}{2}\) then its terminal velocity will be:
1. \(\frac{v}{2}\)
2. \(v\)
3. \(\frac{3v}{2}\)
4. \(2v\)