Some charge is being given to a conductor. Then it's potential:

1.	is maximum at the surface.
2.	is maximum at the centre.
3.	remains the same throughout the conductor.
4.	is maximum somewhere between the surface and the centre.

As per this diagram, a point charge \(\mathrm{+q}\) is placed at the origin \(\mathrm{O}.\) Work done in taking another point charge \(\mathrm{-Q}\) from the point \(\mathrm{A},\) coordinates \((\mathrm{0,a}),\) to another point \(\mathrm{B},\) coordinates \((\mathrm{a,0}),\) along the straight path \(\mathrm{AB}\) is:

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

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. \(\frac{4 \pi \varepsilon_{0} m u^{2}}{q Q}\)

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

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)

The electrostatic potential on the surface of a charged conducting sphere is \(100~\text{V}\). Two statements are made in this regard.

Which of the following is a correct statement?

Consider a uniform electric field in the \(\mathrm{z}\)-direction. The potential is a constant:

a.	in all space.
b.	for any \(\mathrm{x}\) for a given \(\mathrm{z}.\)
c.	for any \(\mathrm{y}\) for a given \(\mathrm{z}.\)
d.	on the \(\mathrm{x-y}\) plane for a given \(\mathrm{z}.\)

Choose the correct option: