Properties of EM Waves: Practice Problem & Solution
The electric field of an electromagnetic wave in free space is given by $E = 10\cos(10^7 t + kx)\hat{j} V/m$ where t and x are in second and metres respectively. It can be inferred that 1. The wavelength $\lambda$ is $188.4 m$ 2. The wave number k is $0.33 rad/m$ 3. The wave amplitude is $10 V/m$ 4. The wave is propagating along +x direction Where one of the following pairs of statement is correct? (2010 Mains)
Solution Explained:
To solve this problem, we apply the core principles of Properties of EM Waves. Understanding the underlying formula is key to arriving at the correct answer below:
Comparing with standard form $E = E_0\cos(\omega t + kx)$ , amplitude $E_0 = 10 V/m$ (Statement 3 is correct). Angular frequency $\omega = 10^7 rad/s$ , so wave number $k = \frac{\omega}{c} = \frac{10^7}{3 \times 10^8} = 0.033 rad/m$ . Wavelength $\lambda = \frac{2\pi}{k} = \frac{2\pi}{0.033} \approx 188.4 m$ (Statement 1 is correct). The positive sign indicates propagation in the -x direction. Thus, 1 and 3 are correct.
Leave a Reply