Q. No.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? \(\frac{1}{4\pi \varepsilon _0} = 9\times 10^9~\text{N-m}^2/\text{C}^2\)
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. \(1.28\times 10^{4}~\text{N/C}\)
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 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. \(1.7\times10^{-18}~\text{kg}\)
| 1. | \(10^{-2}~\text{N-m}\) |
2. | \(0\) |
| 3. | \(10^{-1}~\text{N-m}\) |
4. | \(0.01~\text{N-m}\) |
| 1. | \(\frac{Q+q}{4 \pi r_{2}^{2}}\) | 2. | \(\frac{q}{4 \pi r_{1}^{2}}\) |
| 3. | \(\frac{-Q+q}{4 \pi r_{2}^{2}}\) | 4. | \(\frac{-q}{4 \pi r_{1}^{2}}\) |
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. | 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. |
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
An electric dipole is kept in a uniform electric field such that the dipole moment is not collinear with the electric field. It experiences:
| 1. | a force and torque. |
| 2. | a force but no torque. |
| 3. | a torque but no force. |
| 4. | neither a force nor a torque. |
A point charge is placed at the center of the spherical Gaussian surface. The electric flux through the surface is changed if the:
| 1. | sphere is replaced by a cube of the same volume. |
| 2. | sphere is replaced by a cube of half volume. |
| 3. | charge is moved off-centre in the original sphere. |
| 4. | charge is moved just outside the original sphere. |
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 |
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