The electric field at the origin is along the positive x-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. \(\mathrm D\)

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

A dielectric slab is inserted between the plates of an isolated charged capacitor. Which of the following quantities will remain the same?

Choose the correct option:
1. (a), (b)
2. (b) only
3. (c), (a)
4. (a), (d)

When the separation between two charges is increased, the electric potential energy of the charges:

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