Electromagnetic Waves and Their Characteristics

An electromagnetic wave is travelling in a medium with a velocity $\overrightarrow{v}=v\widehat{i}$ . The electric field oscillations, of this electromagnetic wave wave, are along the y – axis.

(a) Identify the direction in which the magnetic field oscillations are taking place, of the electromagnetic wave wave.

(b) How are the magnitudes of the electric and magnetic fields in the electromagnetic wave related to each other?

The electric field of a plane electromagnetic wave propagating along the z-axis varies with time with an amplitude of $2\mathrm{ }\mathrm{V} {\mathrm{m}}^{-1}$. The average energy density of the magnetic field (in $\mathrm{J}\mathrm{ }{\mathrm{m}}^{-3}$) is :

Take: ${\mathrm{\epsilon }}_0=8.854\times {10}^{-12} \mathrm{F} {\mathrm{m}}^{-1}$

Poynting vector of a plane electromagnetic wave propagating in the direction $\hat{k}$ is

Electric field amplitude of electromagnetic wave is $240 {\mathrm{NC}}^{-1}$ and frequency $50 \mathrm{MHz}$, if the wave is propagating along $\mathrm{x}-\mathrm{axis}$ then equation of wave for electric field is

Wavelength of electromagnetic wave $\mathrm{\beta }=8\times {10}^{-6} \sin \left(2\times {10}^{11}\mathrm{t}+300\mathrm{\pi x}\right)$ Tesla.

Electromagnetic waves propagating along $\mathrm{x}-\mathrm{axis}$, the equation for electric field along $\mathrm{y}-\mathrm{axis}$ is expressed as ${\mathrm{E}}_{\mathrm{y}}={\mathrm{E}}_0 \sin 2\mathrm{\pi }\left(\frac{\mathrm{x}}{\mathrm{\lambda }}-\frac{\mathrm{t}}{\mathrm{T}}\right)$, the wave vector is 

An eloctromagnetic wave propagates along z-direction. The corresponding electric ficld is along x-direction. Which of the following is an acceptable direction for the magnetic field, considering $\hat{x},\hat{y}$, and $\hat{z}$ to be the unit vectors in a Cartesian co-ordinate system?

The magnetic field in a travelling electromagnetic wave has a peak value of $20nT$. The peak value of electric field strength is:

Pick the incorrect statement for electromagnetic waves?

Consider an electromagnetic wave propagating in vacuum. Choose the correct statement:

The electric field component of a monochromatic radiation is given by $\overrightarrow{E}=2E_0\widehat{i}\cos kz\cos \omega t$ ,Its magnetic field $\overrightarrow{B}$ is then given by:

Consider an electromagnetic wave propagating in a vacuum. Choose the correct statement.

Magnetic field in a plane electromagnetic wave is given by

$\overrightarrow{B}=B_0\sin \left(kx+\omega t\right)\widehat{\mathrm{j}} \mathrm{T}$
Expression for the corresponding electric field will be:
where $c$ is the speed of light.

During the propagation of electromagnetic wave in a particular medium :-

In electromagnetic theory, the electric and magnetic phenomena are related to each other. Therefore, the dimensions of electric and magnetic quantities must also be related to each other. In the questions below, $\left[\mathrm{E}\right]\mathrm{ }\mathrm{and}\mathrm{ }\left[\mathrm{B}\right]$ stand for dimensions of electric and magnetic fields respectively, while $\left[{\mathrm{ϵ}}_0\right]\mathrm{ }\mathrm{and} \left[{\mathrm{\mu }}_0\right]\mathrm{ }$ stand for dimensions of the permittivity and permeability of free space respectively. $\left[\mathrm{L}\right] \mathrm{and}\mathrm{ }\left[\mathrm{T}\right]$ are dimensions of length and time respectively. All the quantities are given in $\mathrm{SI}$ units.

The relation between $\left[\mathrm{E}\right]\mathrm{ }\mathrm{and}\mathrm{ }\left[\mathrm{B}\right]$ is

A potassium surface is placed $75 \mathrm{cm}$ away from a $100 \mathrm{W}$ bulb. It is found that the energy radiated by the bulb is $5\%$ of the input power.Consider each $K$-atom as a circular disc of diameter $1 \stackrel{\circ }{\mathrm{A}}$ Determine the time (in $\times {10}^{-1} \mathrm{s}$) required for each atom to absorb an amount of energy equal to its work function of $2.0 \mathrm{eV}$ considering wave nature of light.

A potassium surface is placed $75 \mathrm{cm}$ away from a $100 \mathrm{W}$ bulb. It is found that the energy radiated by the bulb is $5\%$ of the input power. Consider each K-atom as a circular disc of radius $1 \stackrel{°}{\mathrm{A}}$. Determine the time (in ${10}^{-1} \mathrm{s}$) required for each atom to absorb an amount of energy equal to its work function of $2.0 \mathrm{eV}$ considering wave nature of light.

$\left(\text{Use}, e=1.6\times {10}^{-19}\right)$

A tube of length $30 \mathrm{cm}$ has its inner lateral surface blackened. Two lenses of focal lengths $10 \mathrm{cm}$ and $20 \mathrm{cm}$ are fixed at the ends of the tube. For same beam, intensities of spots on screen are $I_1$ and $I_2$ for arrangement $\left(1\right)$ and arrangement $\left(2\right)$. If the ratio of $I_2 : I_1$ is of the form $N^2\text{,}$ find $N$.

Calculate the amplitude of electric field (in $\mathrm{N} {\mathrm{C}}^{-1}$) in a parallel beam of light of intensity $4 \mathrm{W} {\mathrm{m}}^{-2}$.