'$$\mathrm{F}$$' is the force between the two identical charged particles placed at a distance '$$\mathrm{Y}$$' from each other. If the distance between the charges is reduced to half the previous distance then force between them becomes

A uniformly charged semicircular arc of radius '$$r$$' has linear charge density $$(\lambda)$$, is the electric field at its centre? ( $$\in_0=$$ permittivity of free space)

A hollow charged metal sphere has radius 'R'. If the potential difference between its surface and a point at a distance '5 R' from the centre is $$\mathrm{V}$$, then magnitude of electric field Intensity at a distance '5R' from the centre of sphere is

An electric dipole having dipole moment $$\mathrm{P}=\mathrm{q} \times 2 \ell$$ is placed in a uniform electric field '$$\mathrm{E}$$'. The dipole moment is along the direction of the field. The force acting on it and its potential energy are respectively