Question:
In a plane electromagnetic wave, the magnetic field is given by \(\mathbf{B} = 3 \times 10^{-7} \sin (100 \pi x + 10^{12} t)\, T\), then the wavelength of the wave is
(In the equation \(x\) is in metre and \(t\) is in seconds)
In a plane electromagnetic wave, the magnetic field is given by \(\mathbf{B} = 3 \times 10^{-7} \sin (100 \pi x + 10^{12} t)\, T\), then the wavelength of the wave is
(In the equation \(x\) is in metre and \(t\) is in seconds)
Show Hint
Use the wave number \(k\) to find wavelength by \(\lambda = \frac{2 \pi}{k}\).
Updated On: Mar 18, 2026
- 0.02 m
- 0.2 m
- 0.4 m
- 0.04 m
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The Correct Option is A
Solution and Explanation
Step 1: Identify wave number \(k\)
Wave equation form: \[ B = B_0 \sin (k x + \omega t) \] Given \(k = 100 \pi\).
Step 2: Calculate wavelength \(\lambda\)
\[ k = \frac{2 \pi}{\lambda} \implies \lambda = \frac{2 \pi}{k} = \frac{2 \pi}{100 \pi} = \frac{2}{100} = 0.02\, m \] Step 3: Conclusion
Wavelength of the wave is 0.02 m.
Wave equation form: \[ B = B_0 \sin (k x + \omega t) \] Given \(k = 100 \pi\).
Step 2: Calculate wavelength \(\lambda\)
\[ k = \frac{2 \pi}{\lambda} \implies \lambda = \frac{2 \pi}{k} = \frac{2 \pi}{100 \pi} = \frac{2}{100} = 0.02\, m \] Step 3: Conclusion
Wavelength of the wave is 0.02 m.
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