Recent activity in Maxwell's Equations

The intrinsic impedance of a lossy dielectric medium is given by$\frac{j \omega \mu}{\sigma}$$\frac{j \omega \varepsilon}{\mu}$$\sqrt{\frac{j \omega \mu}{\sigma+j \omega ...

A material is described by the following electrical parameters as a frequency of $10 \; \mathrm{GHz}, \sigma=10^{6} \mathrm{mho} / \mathrm{m}, \mu=\mu^{0}$ and $\sigma / ...

While you are listening to a programme from a radio, if a near-by electric light bulb is switched on or switched off, you hear a momentary noise in your radio. This is du...

Consider the periodic square wave in the figure shown. The ratio of the power in the $7^{th}$ harm...

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...

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Two particles of masses $M_{1}$ and $M_{2}\left(M_{1}>M_{2}\right)$ attract each other with a force inversely proportional to the square of the distance between them. The...

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}}...

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 out...

For a uniformly charged sphere of radius $R$ and charge density $\rho$, the ratio of magnitude of electric fields at distances $R / 2$ and $2 R$ from the centre, i.e., $\...

In the infinite plance, $y=6 \mathrm{~m}$, there exists a uniform surface charge density of $(1600 \; \pi)$ $\mu \mathrm{C} / \mathrm{m}^{2}$. The associated electric fie...

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 c...

A system of three electric charges lying in a straight line is in equilibrium. Two of the charges are positive with magnitudes $Q$ and $2 Q$, and are $50 \mathrm{~cm}$ ap...

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)...

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 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} /...

The modes in a rectangular waveguide are denoted by $\mathrm{TE}_{\mathrm{mn}} / \mathrm{TM}_{\mathrm{mn}}$ where $\mathrm{m}$ and $\mathrm{n}$ are the eigen numbers alon...

Consider the following statements regarding the complex Poynting vector $\vec{P}$ for the power radiated by a point source in an infinite homogeneous and lossless medium....

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 \...

Two infinitely long wires carrying current are as shown in the figure below. One wire is in the $y-z$ plane and parallel to the $y$-axis. The other wire is in the $x-y$ p...

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...

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...

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{...

The $\vec{E}$ field in a rectangular waveguide of inner dimensions $a \times b$ is given by\[ \vec{E}=\frac{\omega \mu}{h^{2}}\left(\frac{\pi}{a}\right) H_{0} \sin \left(...

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...

A mast antenna consisting of a $50$ meter long vertical conductor operates over a perfectly conducting ground plane. It is base-fed at a frequency of $600-\mathrm{kHz}$. ...

Which one of the following does represent the electric field lines for the $\mathrm{TE}_{\mathrm{O}_{2}}$ mode in the cross-section of a hollow rectangular metallic waveg...

A parallel plate air-filled capacitor has plate area of $10^{-1} \mathrm{~m}^{2}$ and plate separation of $10^{-3} \mathrm{~m}$. It is connected to a $0.5 \mathrm{~V}, 3....

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}_...

The depth of penetration of electromagnetic wave in a medium having conductivity $\sigma$ at a frequency of $1 \; \mathrm{MHz}$ is $25 \mathrm{~cm}$. The depth of penetra...