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:

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.
                       

A capacitor of capacitance \(C\) is charged to a potential \(V.\) The flux of the electric field through a closed surface enclosing the capacitor is:

Two capacitors each having capacitance \(C\) and breakdown voltage \(V\) are joined in series. The capacitance and the breakdown voltage of the combination will be:   
1. \(2C\) and \(2V\)
2. \(\dfrac{C}{2}\) and \(\dfrac{V}{2}\)
3. \(2C\) and \(\dfrac{V}{2}\)
4. \(\dfrac{C}{2}\) and \(2V\)

          
1. \(C\)
2. \(2C\)
3. \(\dfrac{C}{2}\)
4. none of these

A dielectric slab is inserted between the plates of an isolated capacitor. The force between the plates will: 
1. increase
2. decrease
3. remain unchanged
4. become zero

The energy density in the electric field created by a point charge falls off with the distance from the point charge as:
1. \(\dfrac{1}{r}\)

2. \(\dfrac{1}{r^2}\)

3. \(\dfrac{1}{r^3}\)

4. \(\dfrac{1}{r^4}\)