A dipole comprises of two charged particles of identical magnitude $$q$$ and opposite in nature. The mass 'm' of the positive charged particle is half of the mass of the negative charged particle. The two charges are separated by a distance '$$l$$'. If the dipole is placed in a uniform electric field '$$\bar{E}$$'; in such a way that dipole axis makes a very small angle with the electric field, '$$\bar{E}$$'. The angular frequency of the oscillations of the dipole when released is given by:

For a uniformly charged thin spherical shell, the electric potential (V) radially away from the centre (O) of shell can be graphically represented as -

Let $$\sigma$$ be the uniform surface charge density of two infinite thin plane sheets shown in figure. Then the electric fields in three different region $$E_{I}, E_{I I}$$ and $$E_{I I I}$$ are: