Question

The oscillating magnetic field in a plane electromagnetic wave is given by: $B_y=\left(8\times {10}^{-6}\right)\sin \left[2\times {10}^{11}t+300\pi x\right]T$. Calculate the wavelength of the electromagnetic wave.

Answer 1

Step 1: Given data

$B_y=\left(8\times {10}^{-6}\right)\sin \left[2\times {10}^{11}t+300\pi x\right]T$

Standard equation of magnetic field

$B_y=B_0\sin \left(\omega t+kx\right)T$

Here,

k is the relative permeability.

Magentic field, $B_0=\left(8\times {10}^{-6}\right)\text{T}$

Constant, $k=300\pi$

$\omega =2\times {10}^{11}\frac{\text{rad}}{\text{s}}$

Step 2: To find

We have to find the wavelength.

Step 3: Calculate wavelength

$$\begin{gathered} \lambda =\frac{2\pi }{k} \\ =\frac{2\pi }{300\pi } \\ =\frac{1}{150}\text{m} \\ =0.0067\text{m} \\ =6.7\text{mm} \end{gathered}$$

Therefore, the wavelength will be $6.7\text{mm}$.