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# Question and Answer

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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## QuestionPhysicsClass 12

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.

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,$$\nu=\frac {1.5\times 10^{11}}{2\pi}=23.9\mathit{GHz}$$