Q. No.Two parallel infinite line charges with linear charge densities \(+\lambda~\text{C/m}\) and \(+\lambda~\text{C/m}\) are placed at a distance \({R}.\) The electric field mid-way between the two line charges is:
1.
\(\frac{\lambda}{2 \pi \varepsilon_0 {R}}~\text{N/C}\)
2.
zero
3.
\(\frac{2\lambda}{ \pi \varepsilon_0 {R}} ~\text{N/C}\)
4.
\(\frac{\lambda}{ \pi \varepsilon_0 {R}}~\text{N/C}\)
| 1. | \(\frac{4F}{3}\) | 2. | \(F\) |
| 3. | \(\frac{9F}{16}\) | 4. | \(\frac{16F}{9}\) |
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 \(r>R\). |
A sphere encloses an electric dipole with charges \(\pm3\times10^{-6}~\text C.\) What is the total electric flux through the sphere?
1. \(-3\times10^{-6}~\text{N-m}^2/\text C\)
2. zero
3. \(3\times10^{-6}~\text{N-m}^2/\text C\)
4. \(6\times10^{-6}~\text{N-m}^2/\text C\)
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 centre of the sphere?
\(\left(\frac{1}{4\pi \varepsilon _0} = 9\times 10^9~\text{N-m}^2/\text{C}^2\right)\)
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. \(1.28\times 10^{4}~\text{N/C}\)
(\(r\gg\) 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. | \(\overrightarrow{E}=-\dfrac{\overrightarrow{P}}{4\pi \varepsilon _{0}r^{3}}\) |
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. \( 10^{25} ~\text{m/s}^2\)
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. |
A dipole is placed in an electric field as shown. In which direction will it move?
| 1. | towards the left as its potential energy will decrease. |
| 2. | towards the right as its potential energy will increase. |
| 3. | towards the left as its potential energy will increase. |
| 4. | towards the right as its potential energy will decrease. |
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. | \(\dfrac{1}{{R}^{4}}\) |
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