Recent questions tagged maxwell-equations

A square metal sheet of $4 \mathrm{~m} \times 4 \mathrm{~m}$ is placed on the $x-y$ plane as shown in the figure below.If the surface charge density (in $\mu \mathrm{C} /...

An electric field of $0.01 \mathrm{~V} / \mathrm{m}$ is applied along the length of a copper wire of circular cross-section with diameter $1 \: \mathrm{mm}$. Copper has a...

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

Given $\mathrm{E}=10 e^{-f(4 x-k t)} \bar{y} \; \mathrm{V} / \mathrm{m}$ in free space:Write all the four Maxwell's equations in free space.Find $\nabla \times E$.Find $\...

Identify which one of the following will $\text{NOT}$ satisfy the wave equation.$50 \; e^{f(\omega t-3 z)}$$\sin [\omega(10 z+5 t)]$$\cos \left(y^{2}+5 t\right)$$\sin (x)...

A plane wave in free space with $\vec{E}=(\sqrt{\pi})(10.0$ $\left.\hat{x}+11.8 \hat{y}) \cdot \exp j\left(4 \pi \times 10^{8} t-k z\right)\right]$,where $\hat{x}$ and $\...

Consider a parallel plate waveguide with plate separation $d$ as shown in the figure electric and magnetic fields for the TEM-mode are given by$\begin{array}{l}\mathrm{E}...

The Maxwell equation $\mathrm{V} \times \mathrm{H}=\mathrm{J}+\frac{\partial \overline{D}}{\partial t}$ is based onAmpere's lawGauss' lawFaraday's lawCoulomb's law

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 lo...

The unit of $\nabla \times \mathrm{H}$ isAmpereAmpere/meterAmpere/meter ${ }^{2}$Ampere-meter

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}_...

$\nabla \times \nabla \times \mathrm{P},$ where $\mathrm{P}$ is a vector, is equal to$\mathrm{P} \times \nabla \times \mathrm{P}-\nabla^{2} \mathrm{P}$$\nabla^{2} \text{P...

A medium is divided into regions I and II about $x=0$ plane, as shown in the figure below. An electromagnetic wave with electric field $\mathrm{E}_{1}=4 \hat{a}_{x}+3 \ha...

If $\mathrm{C}$ is a closed curve enclosing a surface $S$, then the magnetic field intensity $\vec{H}$, the current density $\vec{J}$ and the electric flux density $\vec{...

For static electric and magnetic fields in an inhomogeneous source-free medium, which of the following represents the correct form of two of Maxwell's equations?$\begin{a...

A magnetic field in air is measured to be\[ \vec{B}=B_{0}\left(\frac{x}{x^{2}+y^{2}} \hat{y}-\frac{y}{x^{2}+y^{2}} \hat{x}\right) \]What current distribution leads to thi...

The electric field component of a time harmonic plane $\text{EM}$ wave traveling in a nonmagnetic lossless dielectric medium has an amplitude of $1 \; \mathrm{V/m}$. If t...

The electric and magnetic fields for a $\text{TEM}$ wave of frequency $14 \; \mathrm{GHz}$ in a homogeneous medium of relative permittivity $\varepsilon_r$ and relative p...

A current sheet $\vec{J}=10 \hat{u}_y \; A / m$ lies on the dielectric interface $x=0$ between two dielectric media with $\varepsilon_{r 1}=5, \mu_{r 1}=1$ in Region-$1 \...

Concentric spherical shells of radii $2$m, $4$m, and $8$ m carry uniform surface charge densities of $20 \: nC/m^2$, $ – 4 \: nC/m^2$ and $\rho_s$ respectively. The value...

The force on a point charge $+q$ kept at a distance $d$ from the surface of an infinite grounded metal plate in a medium of permittivity $\epsilon\:$ is$0$$\dfrac{q^{2}}...