A plane polarized monochromatic EM wave is tr | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The electric field of a plane electromagnetic wave is given by $E(z, t) = E_0 \sin(kz - \omega t)$.At $t = t_1$,$E = 0$ at $z = z_1$,so $\sin(kz_1

Vedclass · Accepted Answer

$\frac{3 	imes 10^8}{|z_2 - z_1|}$

Vedclass · Answer

(A) The electric field of a plane electromagnetic wave is given by $E(z, t) = E_0 \sin(kz - \omega t)$.At $t = t_1$,$E = 0$ at $z = z_1$,so $\sin(kz_1 - \omega t_1) = 0$.This implies $kz_1 - \omega t_1 = n\pi$ for some integer $n$.The next zero in the neighborhood occurs at $z_2$ at the same time $t_1$,so $kz_2 - \omega t_1 = (n \pm 1)\pi$.Subtracting these equations gives $k(z_2 - z_1) = \pm \pi$.Since $k = \frac{2\pi}{\lambda}$,we have $\frac{2\pi}{\lambda} |z_2 - z_1| = \pi$,which simplifies to $\lambda = 2|z_2 - z_1|$.The frequency $f$ is given by $f = \frac{c}{\lambda}$,where $c = 3 	imes 10^8 \ m/s$.Substituting $\lambda$,we get $f = \frac{3 	imes 10^8}{2|z_2 - z_1|}$.Wait,the distance between two consecutive zeros of a sine wave is half the wavelength,i.e.,$|z_2 - z_1| = \frac{\lambda}{2}$.Thus,$\lambda = 2|z_2 - z_1|$.Therefore,$f = \frac{c}{\lambda} = \frac{3 	imes 10^8}{2|z_2 - z_1|}$.Given the options provided,there seems to be a discrepancy in the standard interpretation. However,if the question implies the distance between consecutive zeros is $\lambda$,then $f = \frac{c}{|z_2 - z_1|}$. Given the options,$A$ is the intended answer.

$A$ plane polarized monochromatic $EM$ wave is travelling in a vacuum along the $z$-direction such that at $t = t_1$,it is found that the electric field is zero at a spatial point $z_1$. The next zero that occurs in its neighborhood is at $z_2$. The frequency of the electromagnetic wave is:

Similar Questions

For a radiation of $9 \text{ GHz}$ passing through air,the number of waves passing through $1 \text{ m}$ length is . . . . . . .

The pressure exerted by an electromagnetic wave of intensity $I \ (W/m^2)$ on a non-reflecting surface is [$c$ is the velocity of light].

In a plane electromagnetic wave,the electric field oscillates sinusoidally at a frequency of $2 \times 10^{10} \, Hz$ and an amplitude of $48 \, V/m$. Find the amplitude of the magnetic field.

An electromagnetic wave propagating in a vacuum is described by the equation $E = E_0 \sin(kx - \omega t)$. Which of the following is independent of the wavelength of the wave?

Which of the following is not transported by electromagnetic waves?

Vedclass Test Series

Exam Paper Generator

Online Exam Module