Q. No.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. \(0.7\times10^{-18}~\text{kg}\)
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. | \(0.01~\text{N-m}\) |
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 \(r>R\). |
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? \(\frac{1}{4\pi \varepsilon _0} = 9\times 10^9~\text{N-m}^2/\text{C}^2\)
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. \(1.28\times 10^{4}~\text{N/C}\)
| 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 \(\frac{-Q}{\varepsilon_0}\). |
| b. | field on the surface of the sphere is \(\frac{-Q}{4\pi \varepsilon_0 R^2}.\) |
| 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 electric field at a point on the equatorial plane at a distance \(r\) from the centre of a dipole having dipole moment \(\overrightarrow{P}\) is given by:
(\(r\gg\) separation of two charges forming the dipole, \(\varepsilon_{0} =\) permittivity of free space)
| 1. | \(\overrightarrow{E}=\frac{\overrightarrow{P}}{4\pi \varepsilon _{0}r^{3}}\) | 2. | \(\overrightarrow{E}=\frac{2\overrightarrow{P}}{\pi \varepsilon _{0}r^{3}}\) |
| 3. | \(\overrightarrow{E}=-\frac{\overrightarrow{P}}{4\pi \varepsilon _{0}r^{2}}\) | 4. | \(\overrightarrow{E}=-\frac{\overrightarrow{P}}{4\pi \varepsilon _{0}r^{3}}\) |
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:
( \(\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9~ \text{Nm}^2 \text{C}^{-2}\) )
| 1. | \( 10^{24} ~\text{m/s}^2\) | 2 | \( 10^{23} ~\text{m/s}^2\) |
| 3. | \( 10^{22}~\text{m/s}^2\) | 4. | \( 10^{25} ~\text{m/s}^2\) |
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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