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  • The magnetic field is given by <img alt="\text { By }=2 \times 10^{-7} T \sin \left(0.5 \times 10^3 x+1.5 \times 10^{11} t\right) T" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Ctex

The magnetic field is given by \text { By }=2 \times 10^{-7} T \sin \left(0.5 \times 10^3 x+1.5 \times 10^{11} t\right) T. The value of wavelength and frequency of the wave is:

Option: 1

1.25 \times 10^{-2} \mathrm{~m} \ \& \ 1.2 \times 10^{10} \mathrm{~Hz}


Option: 2

1.25 \times 10^{-2} \mathrm{~m} \ \& \ 2.4 \times 10^{10} \mathrm{~Hz}


Option: 3

2.5 \times 10^{-2} \mathrm{~m} \ \& \ 2.4 \times 10^{10} \mathrm{~Hz}


Option: 4

2.5 \times 10^{-2} \mathrm{~m} \ \& \ 1.2 \times 10^{10} \mathrm{~Hz}


Answers (1)

best_answer

From the equation

\begin{aligned} & \quad k=0.5 \times 10^3 \mathrm{~m}^{-1} \\ & \because k=\frac{2 \pi}{\lambda} \quad \Rightarrow \lambda=\frac{2 \pi}{k}=\frac{2 \pi}{0.5 \times 10^3}=4 \pi \times 10^{-3} \\ & \Rightarrow \lambda=1.25 \times 10^{-2} \mathrm{~m} \end{aligned}
Also from the equation
\begin{gathered} \omega=1.5 \times 10^{11} \mathrm{rad} / \mathrm{s}=2 \pi \mathrm{f} . \\ \Rightarrow f=\frac{\omega}{2 \pi}=\frac{1.5 \times 10^{11}}{2 \pi}=2.39 \times 10^{10} \mathrm{~Hz} . \end{gathered}
 

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Gaurav

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