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Question

(A) The general equation for a plane electromagnetic wave is given by $\vec{B} = B_0 \sin (kx + \omega t)$.Comparing this with the given equation $\ve

Vedclass · Accepted Answer

$0.02$

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(A) The general equation for a plane electromagnetic wave is given by $\vec{B} = B_0 \sin (kx + \omega t)$.Comparing this with the given equation $\vec{B} = 3 	imes 10^{-7} \sin (100 \pi x + 10^{12} t)$,we identify the wave number $k = 100 \pi \ m^{-1}$.The relationship between the wave number $k$ and the wavelength $\lambda$ is given by $k = \frac{2 \pi}{\lambda}$.Substituting the value of $k$: $100 \pi = \frac{2 \pi}{\lambda}$.Solving for $\lambda$: $\lambda = \frac{2 \pi}{100 \pi} = \frac{2}{100} = 0.02 \ m$.Therefore,the wavelength of the wave is $0.02 \ m$.

In a plane electromagnetic wave,the magnetic field is given by $\vec{B} = 3 \times 10^{-7} \sin (100 \pi x + 10^{12} t) \ T$. The wavelength of the wave is (where $x$ is in meters and $t$ is in seconds). (in $m$)

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