Question

The oscillating magnetic field in a plane electromagnetic wave is given by \(B_y = (8 \times 10^{-6}) \sin[2 \pi \times 10^{11} t + 200 \pi x] \) tesla. Then the wavelength of the electromagnetic wave (in cm) is:

• A. 1
• B. 2
• C. 3
• D. 4
• E. 5

Hint:

The wavelength is the spatial period of the wave, the distance over which the wave's shape repeats.

Answer 1

The Correct Option is A

The angular wave number \(k\) in the equation for the magnetic field component \(B_y\) is \(200\pi\), which is related to the wavelength \(\lambda\) by \( k = \frac{2\pi}{\lambda} \): \[ \frac{2\pi}{\lambda} = 200\pi \implies \lambda = \frac{2\pi}{200\pi} = \frac{1}{100} { m} = 1 { cm} \]