The magnetic field of a beam emerging from a filter facing a floodlight is given by $B = 12 \times 10^{-8} \sin(1.20 \times 10^7 z - 3.60 \times 10^{15} t) \text{ T}$. What is the average intensity of the beam?

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(A) Comparing the given equation $B = 12 \times 10^{-8} \sin(1.20 \times 10^7 z - 3.60 \times 10^{15} t) \text{ T}$ with the standard wave equation,the amplitude of the magnetic field is $B_0 = 12 \times 10^{-8} \text{ T}$.
The average intensity $I_{\text{avg}}$ of an electromagnetic wave is given by the formula:
$I_{\text{avg}} = \frac{B_0^2}{2\mu_0} c$
Substituting the values $B_0 = 12 \times 10^{-8} \text{ T}$,$c = 3 \times 10^8 \text{ m/s}$,and $\mu_0 = 4\pi \times 10^{-7} \text{ T m/A}$:
$I_{\text{avg}} = \frac{(12 \times 10^{-8})^2 \times 3 \times 10^8}{2 \times 4\pi \times 10^{-7}}$
$I_{\text{avg}} = \frac{144 \times 10^{-16} \times 3 \times 10^8}{8\pi \times 10^{-7}}$
$I_{\text{avg}} = \frac{432 \times 10^{-8}}{25.12 \times 10^{-7}} \approx 1.72 \text{ W/m}^2$.

Explore More

Similar Questions

For which of the following media will the wave propagation occur without experiencing attenuation?

In a plane $EM$ wave,the electric field oscillates sinusoidally at a frequency of $30 \text{ MHz}$ and amplitude $150 \text{ V/m}$. Identify the correct expression for $\vec{B}$ assuming the wave is propagating along the $x$-axis and the electric field is oscillating along the $y$-axis.

If the amplitude of the magnetic field component of an electromagnetic wave in vacuum is $B_m = 510 \, nT$,then the amplitude of the electric field component of the wave is ......

Give the relation between vacuum permittivity $(\epsilon_{0})$, vacuum permeability $(\mu_{0})$, and the speed of light $(c)$.

What is the wavelength of light with a frequency of $100\;Hz$?

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo