Plane Wave

The electric field of a monochromatic plane wave travelling in a lossless isotropic and homogenous medium is given by $\vec{E}(z,t) = E_0[\hat{x}cos(\omega t - kz) + \hat{y}sin(\om...

A uniform plane wave with electric field $\vec{E}(x) = A_y\hat{a}_y e^{-j\frac{2\pi x}{3}}$ V/m is travelling in the air (relative permittivity, $\epsilon_r = 1$ and relative perme...

A uniform plane wave with electric field $\vec{E}(x)=A_y \hat{a}_y e^{-j \frac{2 \pi x}{3}} \mathrm{~V} / \mathrm{m}$ is travelling in the air (relative permittivity, $\dot{o}_r=1$...

The electric field of a plane electromagnetic wave is $$E = {a_x}{C_{1x}}\cos (\omega t - \beta z) + {a_y}{C_{1y}}\cos (\omega t - \beta z + \theta )$$ V/m. Which of the following...

Consider a rectangular coordinate system $(x, y, z)$ with unit vectors $a_x, a_y$ and $a_z$. A plane wave traveling in the region $z \geq 0$ with electric field vector $E=10 \cos \...

The expression for an electric field in free space is $$E = {E_0}\left( {\widehat x + \widehat y + j2\widehat z} \right){e^{ - j\left( {\omega t - kx + ky} \right)}},$$ where $$x,{...

Let the electric field vector of a plane electromagnetic wave propagating in a homogenous medium be expressed as $$E = \widehat x{E_x}\,{e^{ - j\left( {wt - \beta z} \right)}},$$ ,...

The electric field of a uniform plane wave travelling along the negative $$z$$ direction is given by the following equation: $$$\overrightarrow E {}_w^i = \left( {{{\widehat a}_{_x...

The electric field intensity of a plane wave traveling in free space is given by the following expression $$E\left( {x,t} \right) = {\widehat a_{_y}}24\pi \,\,\cos \left( {\omega t...

The electric field intensity of a plane wave propagating in a lossless non-magnetic medium is given by the following expression $$\overrightarrow E \left( {z,t} \right) = {\widehat...

The electric field component of a plane wave traveling in a lossless dielectric medium is given by $$$\overrightarrow E \left( {z,t} \right) = {\widehat a_y}2\cos \left( {{{10}^8}t...

Assume that a plane wave in air with an electric field $$\overrightarrow E = 10\cos \left( {\omega t - 3x - \sqrt {3z} } \right){\widehat a_{_y}}\,\,\,V/m$$ is incident on a non-ma...

If the electric field of a plane wave is $$$\overrightarrow E \left( {z,t} \right) = \widehat x3\cos \left( {\omega t - kz + {{30}^ \circ }} \right) - \widehat y4\sin \left( {\omeg...

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...

A plane wave of wavelength $$\lambda $$ is traveling in a direction making an angle $${{{30}^ \circ }}$$ with positive $$x$$-axis and $${{{90}^ \circ }}$$ with positiv $$y$$-axis....

The $$\overrightarrow H $$ field (in A/m) of a plane wave propagating in free space is given by $$$\overrightarrow H = \widehat x{{5\sqrt 3 } \over {{\eta _0}}}\cos \left( {\omega...

When a plane wave traveling in free-space is incident normally on a medium having $${\varepsilon _r} = 4.0,$$ the fraction of power transmitted into the medium is given by

The magnetic field intensity vector of a plane wave is given by $$\overline H \left( {x,y,z,t} \right) = 10\,\sin \left( {50000t + 0.004x + 30} \right){\mathop a\limits^ \cap _y}$$...

A plane wave is characterized by $$$\overrightarrow E = \left( {0.5\mathop x\limits^ \cap + \mathop y\limits^ \cap \,{e^{j\pi /2}}} \right){e^{j\omega t - jkz}}.$$$ This wave is

If a plane electromagnetic wave satisfies the equation $${{{\partial ^2}\,{E_x}} \over {\partial \,{z^2}}} = \,{c^2}{{{\partial ^2}\,{E_x}} \over {\partial \,{t^2}}},$$ the wave pr...

A uniform plane electromagnetic wave incident normally on a plane surface of a dielectric material is reflected with a VSWR of 3. What is the percentage of incident power that is r...

A uniform plane wave in air impinges at 45° angle on a lossless dielectric material with dielectric constant $${\varepsilon _r}$$. The transmitted wave propagates in a 30° directio...

The electric field vector of a wave is given as $$$\vec E = {E_0}{\mkern 1mu} {e^{j\left( {\omega t + 3x - 4y} \right)}}{\mkern 1mu} {{8{{\vec a}_x} + 6{{\vec a}_y} + 5{{\vec a}_z}...