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)

• A. 0.02 m
• B. 0.2 m
• C. 0.4 m
• D. 0.04 m

Hint:

Use the wave number \(k\) to find wavelength by \(\lambda = \frac{2 \pi}{k}\).

Answer 1

The Correct Option is A

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.