An infinite plane sheet of charge having uniform surface charge density $$+\sigma_{\mathrm{s}} \mathrm{C} / \mathrm{m}^2$$ is placed on $$x$$-$$y$$ plane. Another infinitely long line charge having uniform linear charge density $$+\lambda_e \mathrm{C} / \mathrm{m}$$ is placed at $$z=4 \mathrm{~m}$$ plane and parallel to $$y$$-axis. If the magnitude values $$\left|\sigma_{\mathrm{s}}\right|=2\left|\lambda_{\mathrm{e}}\right|$$ then at point $$(0,0,2)$$, the ratio of magnitudes of electric field values due to sheet charge to that of line charge is $$\pi \sqrt{n}: 1$$. The value of $$n$$ is _________.
Then the charge on the particle will be $\frac{1}{\sqrt{x}} \mu \mathrm{C}$ where $x=$ ___________ . [use $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$ ]
(Take density of water $=1 \mathrm{~g} / \mathrm{cc}$ )
The distance between charges $$+q$$ and $$-q$$ is $$2 l$$ and between $$+2 q$$ and $$-2 q$$ is $$4 l$$. The electrostatic potential at point $$P$$ at a distance $$r$$ from center $$O$$ is $$-\alpha\left[\frac{q l}{r^2}\right] \times 10^9 \mathrm{~V}$$, where the value of $$\alpha$$ is __________. (Use $$\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9 \mathrm{~Nm}^2 \mathrm{C}^{-2}$$)
