If the magnitude of intensity of electric field at a distance '$$r_1$$' on an axial line and at a distance '$$r_2$$' on an equatorial line due to a given short dipole are equal, then $$r_1: r_2$$, is

Three charges each of value $$+q$$ are placed at the corners of an isosceles triangle $$\mathrm{ABC}$$ of sides $$\mathrm{AB}$$ and $$\mathrm{AC}$$ each equal to $$2 \mathrm{a}$$. The mid points of $$A B$$ and $$A C$$ are $$D$$ and $$E$$ respectively. The work done in taking a charge $$Q$$ from $$D$$ to $$E$$ is ( $$\varepsilon_0=$$ permittivity of free space)

Select the correct statement from the following.

Two point charges '$$q 1$$' and '$$q 2$$' are separated by a distance '$$d$$'. What is the increase in potential energy of the system when '$$q 2$$' is moved towards '$$q 1$$' by a distance '$$\mathrm{x}$$' ? $$(x < d)(\frac{1}{4 \pi \varepsilon_0}=K$$, constant)