Find the amount of work done in rotating an electric dipole, of dipole moment $3.2\times {10}^{-8}\mathrm{ }\mathrm{Cm}$. from its position of stable equilibrium to the position of unstable equilibrium, in a uniform electric field of intensity ${10}^4\mathrm{ }\mathrm{N}/\mathrm{C}.$

An electric dipole consists of two opposite charges each of magnitude $1 \mu \mathrm{C}$ separated by  $2\mathrm{ }\mathrm{cm}.$ The dipole is placed in an external electric field of ${10}^5\mathrm{N}\mathrm{ }{\mathrm{C}}^{-1}.$ Find i   the maximum torque exerted by the field on the dipole ii  the work which the external agent will have to do in turning the dipole through ${180}^o$ starting from the position $\theta =0^o$

Find the capacitance of a conducting sphere of radius $10\mathrm{ }\mathrm{cm}$situated in air. How much charge is required to raise it to a potential of $1000$ volt?

Assuming the earth to be a spherical conductor of radius $6400\mathrm{ }\mathrm{km}$, calculate its capacitance.

N drops of mercury of equal radii and possessing equal charges to combine to form a big drop. Compare the charge, capacitance and potential of the bigger drop with the corresponding quantities of individual drops.

A capacitor of $20 \mu \mathrm{F}$ is charged to a potential of $10\mathrm{ }\mathrm{kV}$. Find the charge accumulated on each plate of the capacitor.
  

A parallel plate air capacitor consists of two circular plates of diameter 8 cm. At what distance should the plates be held so as to have the same capacitance as that of a sphere of diameter 20 cm?

A capacitor of unknown capacitance is connected across a battery of V  volt. A charge of $120 \mu \mathrm{C}$ is stored in it. When the potential across the capacitor is reduced by $40\mathrm{ }\mathrm{V},$ the charge stored in the capacitor becomes $40\mathrm{ }\mathrm{\mu C}.$ Calculate V  and the unknown capacitance. What would have been charge in the capacitor if the voltage is increased by $40\mathrm{ }\mathrm{V}$.

A parallel-plate capacitor has plates of area $200\mathrm{ }{\mathrm{cm}}^2$ and separation between the plates  $1.0\mathrm{mm}.$  What potential difference will be developed if a charge of $1.0\mathrm{ }\mathrm{nC}$ is given to the capacitor?