The insulation property of air breaks down at \(E = 3\times 10^{6}~\text{V/m}\). The maximum charge that can be given to a sphere of diameter \(5\) m is approximately:
1. \(2\times 10^{-5}~\text{C}\)
2. \(2\times 10^{-4}~\text{C}\)
3. \(2\times 10^{-3}~\text{C}\)
4. \(3\times 10^{-3}~\text{C}\)

The dielectric constant of pure water is \(81\). Its permittivity will be: (in MKS units)
1. \(1.02\times 10^{-13}\)
2. \(8.86\times 10^{-12}\)
3. \(7.17\times 10^{-10}\)
4. \(7.8\times 10^{-10}\)

In a circuit, \(5\) C of charge is passed through a battery in a given time. The plates of the battery are maintained at a potential difference of \(12\) V. The work done by the battery is:

Some equipotential surfaces are shown in figure. The electric field at points \(A\), \(B\) and \(C\) are respectively:

A circuit has section \(AB\) as shown in figure. The emf of the cell is \(10\) V. The potential difference \(V_{AB}= 5~\text{V}\). The charge on the capacitor \(C_1\) is:

A charge \(q_1=5 \times 10^{-8} ~\text{C}\) is kept at \(3\) cm from a charge \(q_2=-2 \times 10^{-8} ~\text{C}\). The potential energy of the system relative to the potential energy at infinite separation is:
1. \(3\times 10^{-4}~\text{J}\)
2. \(-3\times 10^{-4}~\text{J}\)
3. \(9\times 10^{-6}~\text{J}\)
4. \(-9\times 10^{-6}~\text{J}\)

Which of the following statements is correct regarding electrostatics of conductors?

A positive charge \(q\) and a negative charge \(-q\) are placed at \(x=-a\) and \(x=+a\) respectively. The variation of \(V\) along \(x\text-\)axis is represented by the graph:

1.		2.
3.		4.