Q. No.(\(r\gg\) separation of two charges forming the dipole, \(\varepsilon_{0} =\) permittivity of free space)
1. \(\overrightarrow{E}=\dfrac{\overrightarrow{P}}{4\pi \varepsilon _{0}r^{3}}\)
2. \(\overrightarrow{E}=\dfrac{2\overrightarrow{P}}{\pi \varepsilon _{0}r^{3}}\)
3. \(\overrightarrow{E}=-\dfrac{\overrightarrow{P}}{4\pi \varepsilon _{0}r^{2}}\)
4. \(\overrightarrow{E}=-\dfrac{\overrightarrow{P}}{4\pi \varepsilon _{0}r^{3}}\)
Two charges \(\pm 10~ \mu \text{C}\) are placed \(5.0\) mm apart. The electric field at a point \(Q\), \(15\) cm away from \(O\) on a line passing through \(O\) and normal to the axis of the dipole, as shown in the figure is:
1. \(2.8 \times 10^5~\text{NC}^{-1}\)
2. \(3.9\times 10^5 ~\text{NC}^{-1}\)
3. \(1.33\times 10^5 ~\text{NC}^{-1}\)
4. \(4.1\times 10^6 ~\text{NC}^{-1}\)
The magnitude of electric field intensity at a distance \({R}~(R \gg L )\) varies as:
| 1. | \(\dfrac{1}{{R}^{6}}\) | 2. | \(\dfrac{1}{{R}^{2}}\) |
| 3. | \(\dfrac{1}{{R}^{3}}\) | 4. | \(\dfrac{1}{{R}^{4}}\) |
| 1. | \(9\times 10^{-6}~\text{C-m}\) | 2. | \(1.8\times 10^{-7}~\text{C-m}\) |
| 3. | \(1.8\times 10^{-6}~\text{C-m}\) | 4. | \(9\times 10^{-7}~\text{C-m}\) |
Polar molecules are the molecules:
| 1. | that acquires a dipole moment only when the magnetic field is absent. |
| 2. | has a permanent electric dipole moment. |
| 3. | has zero dipole moment. |
| 4. | that acquire a dipole moment only in the presence of an electric field due to displacement of charges. |
Two charges \(\pm10~\mu\text{C}\) are placed \(5.0\) mm apart. The electric field at a point \(P\) on the axis of the dipole \(15\) cm away from its centre \(O\) on the side of the positive charge, as shown in the figure is:
| 1. | \(2.7\times10^5~\text{NC}^{-1}\) |
2. | \(4.13\times10^6~\text{NC}^{-1}\) |
| 3. | \(3.86\times10^6~\text{NC}^{-1}\) | 4. | \(1.33\times10^5~\text{NC}^{-1}\) |
A system has two charges, \(q_\mathrm{A} = 2.5 \times 10^{-7}~\text{C}\) and \(q_\mathrm{B} = -2.5 \times 10^{-7}~\text{C}\), is located at points \(\mathrm{A}\): \((0,0,-15~\text{cm})\) and \(\mathrm{B}\): \((0,0,+15~\text{cm})\) respectively. The electric dipole moment of the system is:
| 1. | \(7.5\times 10^{-8}~\text{C-m}\) (along negative z-axis) |
| 2. | \(8.5\times 10^{-8}~\text{C-m}\) (along positive z-axis) |
| 3. | \(5.5\times 10^{-8}~\text{C-m}\) (along positive z-axis) |
| 4. | \(3.5\times 10^{-8}~\text{C-m}\) (along negative z-axis) |
1. \(2\)
2. \(4\)
3. \(6\)
4. \(8\)
An electric dipole is placed in an electric field generated by a point charge.
| (a) | The net electric force on the dipole must be zero. |
| (b) | The net electric force on the dipole may be zero. |
| (c) | The torque on the dipole due to the field must be zero. |
| (d) | The torque on the dipole due to the field may be zero. |
Choose the correct option:
| 1. | (a) only | 2. | (b), (c) |
| 3. | (c), (d) | 4. | (d) only |
An electric dipole is placed at an angle of \(30^{\circ}\) with an electric field of intensity \(2 \times 10^{5}~ \text{N} \text{C}^{-1}\). It experiences a torque equal to \(4~\text{N-m}\). The charge on the dipole, if the dipole length is \(2~\text{cm}\) is:
| 1. | \(8~\text{mC}\) | 2. | \(4~\text{mC}\) |
| 3. | \(6~\text{mC}\) | 4. | \(2~\text{mC}\) |
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