Two equal positive charges are kept at points \(A\) and \(B\). The electric potential at the points between \(A\) and \(B\) (excluding these points) is studied while moving from \(A\) to \(B\). The potential:

1.	continuously increases.
2.	continuously decreases.
3.	increases then decreases.
4.	decreases then increases.

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. \(\mathrm D\)

Consider the situation of the figure. The work done in taking a point charge from \(\mathrm{P}\) to \(\mathrm{A}\) is \(W_{\mathrm{A}}\) , from \(\mathrm{P}\) to \(\mathrm{B}\) is \(W_{\mathrm{B}}\) and from \(\mathrm{P}\) to \(\mathrm{C}\) is \(W_{\mathrm{C}}\). Then:

A point charge \(q\) is rotated along a circle in the electric field generated by another point charge \(Q\). The work done by the electric field on the rotating charge in one complete revolution is:
1. zero.
2. positive.
3. negative.
4. zero if the charge \(Q\) is at the centre and non-zero otherwise.

The electric field and the electric potential at a point are E and V respectively.

(a) If E = 0, V must be zero.

(b) If V = 0, E must be zero.

(c) If E ≠ 0, V cannot be zero.

(d) If V ≠ 0, E cannot be zero

Choose the coorect option 

1. (a) only 

2. (b) , (c) 

3. (c) , (d) 

4. None of these 

The electric potential decreases uniformly from 120 V to 80 V as one moves on the x-axis from x = –1 cm to x = +1 cm. The electric field at the origin

(a) must be equal to 20 V cm^–1

(b) may be equal to 20 V cm^–1

(c) may be greater than 20 V cm^–1

(d) may be less than 20 V cm^–1

Choose the coorect option 

1. (a) only 

2. (b) , (c) 

3. (c) , (d) 

4. (a) , (d) 

Which of the following quantities do not depend on the choice of zero potential or zero potential energy?

(a) potential at a point
(b) potential difference between two points
(c) potential energy of a two-charge system
(d) change in potential energy of a two-charge system.
Choose the correct option: 
1. (a) only 
2. (b), (c) 
3. (b), (d) 
4. (a), (d) 

The electric field in a region is directed outward and is proportional to the distance \(r\) from the origin. Taking the electric potential at the origin to be zero;

Choose the correct option from the given ones:
1. (a) only 
2. (b) and (c) only
3. (c) only 
4. (a) and (d) only

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

1. towards left

2. towards right

3. upward

4. zero.

Previous problem: A thin, metallic spherical shell contains a charge Q on it. A point charge q is placed at the centre of the shell and another charge q₁ is placed outside it as shown in figure. All the three charges are positive.