The magnetic field in a plane electromagnetic wave is given by $B = 3 × 10^{-7}\sin(1.5x + 5 × 10^8t) T$, where x is in meter and t is in second. The wavelength of the wave is: (Take: $π = 3$)
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 4 m
Given magnetic field: $B = 3\times10^{-7}\sin(1.5x + 5\times10^{8}t)$
Standard wave equation: $B = B_0\sin(kx + \omega t)$
Here, $k = 1.5\,\text{rad/m}$ and $\omega = 5\times10^{8}\,\text{rad/s}$
Wavelength: $\lambda = \frac{2\pi}{k}$
Substitute $k = 1.5$ and $\pi = 3$
$\lambda = \frac{2\times3}{1.5} = \frac{6}{1.5} = 4\,\text{m}$
Answer: $\lambda = 4\,\text{m}$