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 ___________.

When a hydrogen atom going from $$n=2$$ to $$n=1$$ emits a photon, its recoil speed is $$\frac{x}{5} \mathrm{~m} / \mathrm{s}$$. Where $$x=$$ ________. (Use, mass of hydrogen atom $$=1.6 \times 10^{-27} \mathrm{~kg}$$)

A square loop of side $$10 \mathrm{~cm}$$ and resistance $$0.7 \Omega$$ is placed vertically in east-west plane. A uniform magnetic field of $$0.20 T$$ is set up across the plane in north east direction. The magnetic field is decreased to zero in $$1 \mathrm{~s}$$ at a steady rate. Then, magnitude of induced emf is $$\sqrt{x} \times 10^{-3} \mathrm{~V}$$. The value of $$x$$ is __________.

The magnetic potential due to a magnetic dipole at a point on its axis situated at a distance of $$20 \mathrm{~cm}$$ from its center is $$1.5 \times 10^{-5} \mathrm{~T} \mathrm{~m}$$. The magnetic moment of the dipole is _________ $$A \mathrm{~m}^2$$. (Given : $$\frac{\mu_o}{4 \pi}=10^{-7} \mathrm{Tm} A^{-1}$$ )