A dielectric slab is inserted between the plates of an isolated charged capacitor. Which of the following quantities will remain the same?
(a) | the electric field in the capacitor |
(b) | the charge on the capacitor |
(c) | the potential difference between the plates |
(d) | the stored energy in the capacitor |
Choose the correct option:
1. (a), (b)
2. (b) only
3. (c), (a)
4. (a), (d)
A thin, metallic spherical shell contains a charge \(\mathrm{Q}\) on it. A point charge \(\mathrm{q}\) is placed at the centre of the shell and another charge \(\mathrm{q}_1\) is placed outside as it is shown in the figure. All the three charges are positive. The force on the charge at the centre is:
1. towards left
2. towards right
3. upward
4. zero
The electric field at the origin is along the positive \(x\text-\)axis. A small circle is drawn with the centre at the origin cutting the axes at points \(\mathrm A\), \(\mathrm B\), \(\mathrm C\) and \(\mathrm D\) having coordinates \((a,0),(0,a),(-a,0),(0,-a)\) respectively. Out of the points on the periphery of the circle, the potential is minimum at:
1. \(\mathrm A\)
2. \(\mathrm B\)
3. \(\mathrm C\)
4. \(\mathrm D\)
When the separation between two charges is increased, the electric potential energy of the charges:
1. | increases |
2. | decreases |
3. | remains the same |
4. | may increase or decrease |
1. | stable in both A, B |
2. | stable in A, unstable in B |
3. | unstable in A, stable in B |
4. | unstable in both A, B |
A positively charged light particle of charge \(q\) and mass \(m\) approaches another heavy particle of positive charge \(Q,\) coming towards it with an initial speed \(u,\) when it is far away.
The distance of the closest approach is given by:
1. \(\frac{q Q}{4 \pi \varepsilon_{0} m u^{2}}\)
2. \(\frac{q Q}{\pi \varepsilon_{0} m u^{2}}\)
3. \(\frac{q Q}{2 \pi \varepsilon_{0} m u^{2}}\)
4. \(\frac{4 \pi \varepsilon_{0} m u^{2}}{q Q}\)
The \(6\) \(\mu\)F capacitor is initially charged to \(2\) V (i.e. \(V_B-V_A=2\) V) while the \(3\) \(\mu\)F capacitor is uncharged. The switch is now closed. The final potential difference across the \(3\) \(\mu\)F capacitor will be:
1. \(4 \) V
2. \(\frac{4}{3} \) V
3. \(2\) V
4. \(\frac{8}{3} \) V
1. | more. |
2. | less. |
3. | equal. |
4. | \(K\). | more or less or equal depending on the value of