An electron is moving under the influence of the electric field of a uniformly charged infinite plane sheet $$\mathrm{S}$$ having surface charge density $$+\sigma$$. The electron at $$t=0$$ is at a distance of $$1 \mathrm{~m}$$ from $$S$$ and has a speed of $$1 \mathrm{~m} / \mathrm{s}$$. The maximum value of $$\sigma$$ if the electron strikes $$S$$ at $$t=1 \mathrm{~s}$$ is $$\alpha\left[\frac{m \epsilon_0}{e}\right] \frac{C}{m^2}$$, the value of $$\alpha$$ is ___________.

Two charges of $$-4 \mu \mathrm{C}$$ and $$+4 \mu \mathrm{C}$$ are placed at the points $$\mathrm{A}(1,0,4) \mathrm{m}$$ and $$\mathrm{B}(2,-1,5) \mathrm{m}$$ located in an electric field $$\overrightarrow{\mathrm{E}}=0.20 \hat{i} \mathrm{~V} / \mathrm{cm}$$. The magnitude of the torque acting on the dipole is $$8 \sqrt{\alpha} \times 10^{-5} \mathrm{Nm}$$, where $$\alpha=$$ _________.

The electric potential at the surface of an atomic nucleus $$(z=50)$$ of radius $$9 \times 10^{-13} \mathrm{~cm}$$ is __________ $$\times 10^6 \mathrm{~V}$$.

A thin metallic wire having cross sectional area of $$10^{-4} \mathrm{~m}^2$$ is used to make a ring of radius $$30 \mathrm{~cm}$$. A positive charge of $$2 \pi \mathrm{~C}$$ is uniformly distributed over the ring, while another positive charge of 30 $$\mathrm{pC}$$ is kept at the centre of the ring. The tension in the ring is ______ $$\mathrm{N}$$; provided that the ring does not get deformed (neglect the influence of gravity). (given, $$\frac{1}{4 \pi \epsilon_0}=9 \times 10^9$$ SI units)