An optical fiber consists of a cylindrical dielectric rod of refractive index $$n_1$$, surrounded by another dielectric of refractive index $$n_2$$ where $$n_2$$ < $$n_1$$ as shown in the following Fig. If a ray is incident from air at angle i to the axis, then it undergoes total internal reflection at the interface AB if

Given,$$\overrightarrow V=x\cos^2y\;\;\widehat{\mathrm i}\;+\;\mathrm x^2\mathrm e^\mathrm z\;\widehat{\mathrm j}\;+\;\mathrm{zsin}^2\mathrm y\;\widehat{\mathrm k}$$ and S the surface of a unit cube with one corner at the origin and edges parallel to the coordinate axes, the value of the integral is

The built-in potential (Diffusion Potential) in a p-n junction

If the linear velocity $${\overrightarrow V }$$ is given by $$\overrightarrow V = {x^2}y\overrightarrow i + xyz\overrightarrow j - y{z^2}\overrightarrow k $$ then the angular velocity $$\overrightarrow W $$ at the point $$\left( {1,1, - 1} \right)$$ is _______.