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The magnetic field in a plane electromagnetic wave is given by \(B=2\times 10^{\text{--}7}T\sin (0.5\times 10^3x+1.5\times 10^{11}t)\) .What is the wavelength and frequency of the wave.
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The magnetic field in a plane electromagnetic wave is given by \(B=2\times 10^{\text{--}7}T\sin (0.5\times 10^3x+1.5\times 10^{11}t)\) .What is the wavelength and frequency of the wave.

Answer

Wavelength \(= 1.26\ cm\)
Frequency\( = 23.9\ GHz\)
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Solution

Given: Magnetic field,\(B=2\times 10^{\text{--}7}\sin (0.5\times 10^3x+1.5\times 10^{11}t)\)
We know that the standard equation of magnetic field for \(EM \)wave
\(B=B_o\sin [2\pi (\frac x{\lambda }+\frac t T)]\)
On comparing this equation with the given equation we get
 \(\frac{2\pi }{\lambda }=0.5\times 10^{-3}\)
Wavelength, \(\lambda =\frac{2\pi }{0.5\times 10^{-3}}=1.26\text{ cm}\)
\(2\pi \nu=1.5\times 10^{11}\)
Frequency,\(\nu=\frac {1.5\times 10^{11}}{2\pi}=23.9\mathit{GHz}\)
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