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# The magnetic field in a plane electromagnetic wave is given by $2\times {{10}^{-7}}\sin (0.5\times {{10}^{3}}x+1.5\times {{10}^{11}}t)$.This electromagnetic wave isA. Visible lightB. InfraredC. MicrowaveD. Radio Wave

Last updated date: 17th Sep 2024
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Hint: the above equation is of electromagnetic wave, by equating the above equation with the standard equation of electromagnetic wave we need to find wavelength, and by comparing it in the electromagnetic spectrum we can identify the type of waveform.

Formula used:
$E={{E}_{m}}\sin (kx+\omega t)$
$k=\dfrac{2\pi }{\lambda }$.

Complete solution:
The standard electromagnetic wave equation travelling in negative direction of x-axis is given by $E={{E}_{m}}\sin (kx+\omega t)$,

Here, ${{E}_{m}}$(amplitude), $k$(propagation constant), $\omega$(angular frequency) and $t$(time period).

Now, we know that $k=\dfrac{2\pi }{\lambda }$ and from the given equation by comparing $k=0.5\times {{10}^{3}}$ so,
$\dfrac{2\pi }{\lambda }=0.5\times {{10}^{3}}$
$\lambda =\dfrac{2\pi }{0.5\times {{10}^{3}}}=12.56\times {{10}^{-3}}m$

Electromagnetic energy travels in waves and spans a broad spectrum from very long radio waves to very short gamma rays and divided into seven different spectrum, the wavelength range of microwave is 1m to ${{10}^{-3}}m$ so our required range satisfied our wavelength.

Therefore, the answer is option C Microwave.