GATE EC Maxwell's Equations questions

If $\overrightarrow{\mathrm{E}}=\left(\hat{a}_{x}+j \vec{a}_{y}\right) e^{\beta a-k a t}$ and $\overrightarrow{\mathrm{H}}=\left(\frac{k}{\omega \mu}\right)\left(\hat{a}_{y}+j \hat{a}_{x}\right) e^{j u-\mu \mu 1}$, the time averaged Poynting vector is

The unit of $\nabla \times \mathrm{H}$ is

Medium $1$ has the electrical permittivity $\varepsilon_{1}=1.5 \varepsilon_{0}$ farad $/ \mathrm{m}$ and occupies the region to the left of $x=0$ plane. Medium $2$ has the electrical permittivity $\varepsilon_{2}=2.5 \varepsilon_{0}$ farad $/ \mathrm{m}$ and occupies the region to the right of $x=0$ plane. If $\mathrm{E}_{1}$ in medium …

The electric field on the surface of a perfect conductor is $2 \mathrm{~Vm}$. The conductor is immersed in water with $\epsilon=80 \epsilon_{0}$. The surface charge density on the conductor is $\left(\epsilon_{0}=10^{-4} /(36 \pi) \mathrm{F} / \mathrm{m}\right)$

If a plane electromagnetic wave satisfies the equation $\frac{\partial^{2} \mathrm{E}_{\mathrm{x}}}{\partial \mathrm{z}^{2}}=\mathrm{c}^{2} \frac{\partial^{2} \mathrm{E}_{\mathrm{x}}}{\partial \mathrm{t}^{2}}$, the wave propagates in the

A material has conductivity of $10^{-2} \mathrm{mho/m}$ and a relative permittivity of $4.$ The frequency at which the conduction current in the medium is equal to the displacement current is

A $\text{TEM}$ wave is incident normally upon a perfect conductor. The $\mathrm{E}$ and $\mathrm{H}$ fields at the boundary will be, respectively,

Identify which one of the following will $\text{NOT}$ satisfy the wave equation.

An electric field on a plane is described by its potential $$\mathrm{V}=20\left(r^{-1}+r^{-2}\right)$$ where $r$ is the distance from the source. The field is due to

A loop is rotating about the $y$-axis in a magnetic field $\overrightarrow{\mathrm{E}}=\mathrm{B}_{0} \cos (\omega t+\phi) \vec{a}_{x} \mathrm{~T}$. The voltage in the loop is

The time averages Poynting vector, in $W / m^{2}$, for a wave with $\vec{E}=24 \; e^{} \; a_{} \mathrm{~V} / \mathrm{m}$ in free space is

The Maxwell equation $\mathrm{V} \times \mathrm{H}=\mathrm{J}+\frac{\partial \overline{D}}{\partial t}$ is based on

A metal sphere with $1 \mathrm{~m}$ radius and a surface charge density of $10 \; \mathrm{Coulombs / m}^{2}$ is enclosed in a cube of $10 \mathrm{~m}$ side. The total outward electric displacement normal to the surface of the cube is

The electric field strength at a distance point, $\mathrm{P}$, due to a point charge, $+q$. located on the origin, is $100 \; \mu \mathrm{V} / \mathrm{m}$. If the point charge is now enclosed by a perfectly conducting metal sheet sphere whose centre is at the origin, then the electric field strength at the point. $P$. outside the sphere, becomes.