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. | \(10^{-2}~\text{N-m}\) |
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. \(1.7\times10^{-18}~\text{kg}\)
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 spherical conductor of radius \(10~\text{cm}\) has a charge of \(3.2 \times 10^{-7}~\text{C}\) distributed uniformly. What is the magnitude of the electric field at a point \(15~\text{cm}\) from the center of the sphere? \(\dfrac{1}{4\pi \varepsilon _0} = 9\times 10^9~\text{N-m}^2/\text{C}^2\)
1. \(1.28\times 10^{5}~\text{N/C}\)
2. \(1.28\times 10^{6}~\text{N/C}\)
3. \(1.28\times 10^{7}~\text{N/C}\)
4. \(1.28\times 10^{4}~\text{N/C}\)
(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) |
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. |