In a certain charge distribution, all points having zero potential can be joined by a circle \(S.\) The points inside \(S\) have positive potential, and points outside \(S\) have a negative potential. A positive charge, which is free to move, is placed inside \(S.\) What is the correct statement about \(S\):

1.	It will remain in  equilibrium
2.	It can move inside \(S,\) but it cannot cross \(S\)
3.	It must cross \(S\) at some time
4.	It may move, but will ultimately return to its starting point

Two charges \(q_1\) and \(q_2\) are placed \(30~\text{cm}\) apart, as shown in the figure. A third charge \(q_3\) is moved along the arc of a circle of radius \(40~\text{cm}\) from \(C\) to \(D.\) The change in the potential energy of the system is \(\dfrac{q_{3}}{4 \pi \varepsilon_{0}} k,\) where \(k\) is:

If the dielectric constant and dielectric strength be denoted by \(k\) and \(x\) respectively, then a material suitable for use as a dielectric in a capacitor must have:
1. high \(k\) and high \(x\).
2. high \(k\) and low \(x\).
3. low \(k\) and low \(x\).
4. low \(k\) and high \(x\).

Three capacitors of capacitances \(3~\mu\text{F}\), \(9~\mu\text{F}\) and \(18~\mu\text{F}\) are connected once in series and another time in parallel. The ratio of equivalent capacitance in the two cases \(\frac{C_s}{C_p}\) will be:
1. \(1:15\)
2. \(15:1\)
3. \(1:1\)
4. \(1:3\)

Four capacitors each of capacity \(3~\mu\text{F}\) are connected as shown in the adjoining figure. The ratio of equivalent capacitance between \(A\) and \(B\) and between \(A\) and \(C\) will be:

1. \(4:3\)

2. \(3:4\)

3. \(2:3\)

4. \(3:2\)

A parallel plate condenser is filled with two dielectrics as shown. Area of each plate is \(A\) metre² and the separation is \(t\) metre. The dielectric constants are \(k_1\) and \(k_2\) respectively. Its capacitance in farad will be:

        
1. \(\frac{\varepsilon_{0} A}{t} \left( k_{1} + k_{2}\right)\)
2. \(\frac{\varepsilon_{0} A}{t} \frac{\left( k_{1} + k_{2}\right)}{2}\)
3. \(\frac{2\varepsilon_{0} A}{t} \left( k_{1} + k_{2}\right)\)
4. \(\frac{\varepsilon_{0} A}{t} \frac{\left( k_{1} - k_{2}\right)}{2}\)

In the connections shown in the adjoining figure, the equivalent capacity between \(A\) and \(B\) will be:

1. \(10.8~\mu\text{F}\)
2. \(69~\mu\text{F}\)
3. \(15~\mu\text{F}\)
4. \(10~\mu\text{F}\)

The diagrams below show regions of equipotentials.

A capacitor of \(2~\mu\text{F}\) is charged as shown in the figure. When the switch \(S\) is turned to position \(2\), the percentage of its stored energy dissipated is: