Two equal positive point charges are separated by a distance $$2 a$$. The distance of a point from the centre of the line joining two charges on the equatorial line (perpendicular bisector) at which force experienced by a test charge $$\mathrm{q}_{0}$$ becomes maximum is $$\frac{a}{\sqrt{x}}$$. The value of $$x$$ is __________.

Expression for an electric field is given by $$\overrightarrow{\mathrm{E}}=4000 x^{2} \hat{i} \frac{\mathrm{V}}{\mathrm{m}}$$. The electric flux through the cube of side $$20 \mathrm{~cm}$$ when placed in electric field (as shown in the figure) is __________ $$\mathrm{V} \mathrm{~cm}$$.

The value of $n$ is _________ (if dimension of cuboid is $1 \times 2 \times 3 \mathrm{~m}^{3}$ )

For a charged spherical ball, electrostatic potential inside the ball varies with $$r$$ as $$\mathrm{V}=2ar^2+b$$.

Here, $$a$$ and $$b$$ are constant and r is the distance from the center. The volume charge density inside the ball is $$-\lambda a\varepsilon$$. The value of $$\lambda$$ is ____________.

$$\varepsilon$$ = permittivity of the medium