The insulation property of air breaks down at $E$ $=$ $3$ $\times$ ${10}^6$ V/m. The maximum charge that can be given to a sphere of diameter 5 m is approximately:

1.  $2$ $\times {10}^{-5}$ $C$

2.  $2$ $\times {10}^{-4}$ $C$

3.  $2$ $\times {10}^{-3}$ $C$

4.  $3$ $\times {10}^{-\mathrm{3 }}C$ 

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:

The electric potential in a certain region of space is given by V = –8x² + 4x, where V is in volt and x is in metre. In this region, the equipotential surface is:

A circuit has section AB as shown in figure. The emf of the cell is 10 V. The potential difference V_AB= 5 V. The charge on the capacitor C₁ is:

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

1. 3 x ${10}^{-4}$ J

2. –3 x ${10}^{-4}$ J

3. 9 x ${10}^{-6}$ J

4. –9 x ${10}^{-6}$ 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-axis is represented by the graph:

1.		2.
3.		4.

How many capacitors each of $8$ $\mu F$ and 250 V are required to form a composite capacitor of $16$ $\mu F$ and 1 kV?