A plane wave having the electric field component $$${\overrightarrow E _i} = 24\,\,\cos \,\,\left( {3 \times {{10}^8}\,t - \beta \,y} \right){\widehat a_z}\,\,V/m$$$
and traveling in free space is incident normally on a lossless medium with $$\mu = {\mu _0}$$ and $$\varepsilon = 9\,\,{\varepsilon _0},$$ which occupies the region $$y \ge 0.$$ The reflected magnetic field component is given by

If $$\overrightarrow{\mathrm A}\;=\;\mathrm{xy}\;{\widehat{\mathrm a}}_\mathrm x\;+\;\mathrm x^2\;{\widehat{\mathrm a}}_\mathrm y$$ then $$\oint\overrightarrow{\mathrm A}.\overrightarrow{\mathrm d}\mathcal l$$ over the path shown in the figure is

The silicon sample with unit cross-sectional area shown below is in thermal equilibrium. The following information is given: T=300K, electronic charge=1.6x10^{- 19}C, thermal voltage=26mV and electron mobility = 1350cm²/V-s

The magnitude of the electric field at x=0.5 μm is

The silicon sample with unit cross-sectional area shown below is in thermal equilibrium. The following information is given: T=300K, electronic charge=1.6x10^{- 19}C, thermal voltage=26mV and electron mobility = 1350cm²/V-s

The magnitude of the electron drift current density at x=0.5 μm is