A conducting sphere of radius \(R\) is given a charge \(Q\). The electric potential and field at the centre of the sphere respectively are:

1.	Zero and \({Q} / 4 \pi \varepsilon_{0} {R}^2\)
2.	\({Q} / 4 \pi \varepsilon_{0} {R}\) and zero
3.	\({Q} / 4 \pi \varepsilon_{0} {R}\) and \({Q} / 4 \pi \varepsilon_{0}{R}^2\)
4.	Both are zero

Four point charges \(-Q, -q,2q~\text{and}~2Q\) are placed, one at each corner of the square. The relation between \(Q\) and \(q\) for which the potential at the center of the square is zero, is:

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

Five identical plates each of area \(A\) are joined as shown in the figure. The distance between the plates is \(d\). The plates are connected to a potential difference of \(V\) volts. The charge on plates \(1\) and \(4\) will be:

        
1. \(-\frac{\varepsilon_{0} A V}{d} ,  \frac{2\varepsilon_{0} A V}{d}\)
2. \(\frac{\varepsilon_{0} A V}{d} ,  \frac{2\varepsilon_{0} A V}{d}\)
3. \(\frac{\varepsilon_{0} A V}{d} , -\frac{2\varepsilon_{0} A V}{d}\)
4. \(-\frac{\varepsilon_{0} A V}{d} ,  -\frac{2\varepsilon_{0} A V}{d}\)

A network of four capacitors of capacity equal to \(C_1 = C, C_2 = 2C, C_3 = 3C\) and \(C_4 = 4C\) are connected in a battery as shown in the figure. The ratio of the charges on \(C_2\) and \(C_4\) is:
         
1. \(\frac{22}{3}\)
2. \(\frac{3}{22}\)
3. \(\frac{7}{4}\)
4. \(\frac{4}{7}\)

An electric dipole of moment \(p\) is placed in an electric field of intensity \(E\). The dipole acquires a position such that the axis of the dipole makes an angle \(\theta\) with the direction of the field. Assuming that the potential energy of the dipole to be zero when \(\theta = 90^{\circ},\) the torque and the potential energy of the dipole will respectively be:

The equivalent capacitance between points \(a\) and \(b\) in the network shown below is:

1. \(5~\text{C}\)
2. \(4~\text{C}\)
3. \(3~\text{C}\)
4. \(2~\text{C}\)

The equivalent capacitance of the following arrangement is:
               
1. \(18~\mu \text{F}\)
2. \(9~\mu \text{F}\)
3. \(6~\mu \text{F}\)
4. \(12~\mu \text{F}\)

Two capacitors of capacitance \(6~\mu\text{F}\) and \(3~\mu\text{F}\) are connected in series with battery of \(30~\text{V}\). The charge on \(3~\mu\text{F}\) capacitor is:
          
1. \( 3 ~\mu\text{C}\)
2. \( 1.5 ~\mu\text{C}\)
3. \( 60~\mu\text{C}\)
4. \( 900~\mu\text{C}\)

Three charges \(-Q,q,\) and \(-2Q\) are placed along a line as shown in the figure. The system of charges will have a positive potential energy configuration when \(q\) is placed at the midpoint of line joining \(-Q\) and \(-2Q\) if: