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,

(a) it is uniform in the region

(b) it is proportional to r

(c) it is proportional to r²

(d) it increases as one goes away from the origin.

 Choose the coorect option 

1. (a) only 

2. (b) , (c) 

3. (c) only 

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

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:
1. \( CV \over \varepsilon_0\)
2. \(2 CV \over \varepsilon_0\)
3. \( CV \over2 \varepsilon_0\)
4. zero

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. \(C/2\) and \(V/2\)
3. \(2C\) and \(V/2\)
4. \(C/2\) and \(2V\)

          
1. \(C\)
2. \(2C\)
3. \(\frac{C}{2}\)
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. \(1 \over r\)

2. \(1 \over r^2\)

3. \(1 \over r^3\)

4. \(1 \over r^4\)

A parallel-plate capacitor has plates of unequal area. The larger plate is connected to the positive terminal of the battery and the smaller plate to its negative terminal. Let Q₊ and Q_- be the charges appearing on the positive and negative plates respectively.

1.  Q₊ > Q_–

2.  Q₊ = Q_– 

3.  Q₊ < Q_-

4.  The information is not sufficient to decide the relation between Q₊ and Q_–