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. | zero as \(r\) increases for \(r<R\), decreases as \(r\) increases for \(r>R\). |
4. | zero as \(r\) increases for \(r<R\), increases as \(r\) increases for \(r>R\). |
Two point charges \(A\) and \(B\), having charges \(+Q\) and \(-Q\) respectively, are placed at a certain distance apart and the force acting between them is \(F.\) If \(25\%\) charge of \(A\) is transferred to \(B\), then the force between the charges becomes:
1. | \(\frac{4F}{3}\) | 2. | \(F\) |
3. | \(\frac{9F}{16}\) | 4. | \(\frac{16F}{9}\) |
Two parallel infinite line charges with linear charge densities \(+\lambda\) C/m and \(+\lambda\) C/m are placed at a distance \({R}.\) The electric field mid-way between the two line charges is:
1. \(\frac{\lambda}{2 \pi \varepsilon_0 {R}} \) N/C
2. zero
3. \(\frac{2\lambda}{ \pi \varepsilon_0 {R}} \) N/C
4. \(\frac{\lambda}{ \pi \varepsilon_0 {R}}\) N/C
A sphere encloses an electric dipole with charges \(\pm3\times10^{-6}\) C. What is the total electric flux through the sphere?
1. \(-3\times10^{-6}\) N-m2/C
2. zero
3. \(3\times10^{-6}\) N-m2/C
4. \(6\times10^{-6}\) N-m2/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 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. \(1.28\times 10^{4}~\text{N/C}\)
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. | \( 10^{25} ~\text{m/s}^2\) |
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. |
1. | \(\frac{1}{{R}^{6}}\) | 2. | \(\frac{1}{{R}^{2}}\) |
3. | \(\frac{1}{{R}^{3}}\) | 4. | \(\frac{1}{{R}^{4}}\) |