91Ó°ÊÓ

Wavelength is a critical concept when discussing electromagnetic waves, as it determines properties like frequency and energy. Wavelength (\(\lambda\)) is the distance between consecutive peaks of an electromagnetic wave. For this exercise, the wavelength of the wave is provided as 35.4 cm, which can be converted to meters as 0.354 m. The relationship between the speed of light (\(c\)), frequency (\(f\)), and wavelength is described by the equation \[ c = f \cdot \lambda \] From this equation, knowing any two of these values lets you calculate the third. In our exercise, after substituting the known values, we found the frequency to be approximately \(8.47 \times 10^8\) Hz. Understanding this relationship is crucial for solving many wave-related problems across physics.

The electric field amplitude (\(E_0\)) is a measure of the strength of the electric component of an electromagnetic wave. At a distance of 250 meters from the antenna in our scenario, the electric field amplitude is given as \(5.40 \times 10^{-2}\) V/m.The amplitude of the electric field determines the wave’s energy content and is a key quantity in calculating other features of electromagnetic waves, like intensity and magnetic field amplitude. A larger amplitude signifies a more powerful wave, having implications in applications ranging from communications to medical technologies.

The magnetic field amplitude (\(B_0\)) reflects the strength of the magnetic part of the electromagnetic wave. This concept is often discussed alongside the electric field amplitude.In electromagnetic waves, particularly those traveling in vacuum or free space, the electric field amplitude (\(E_0\)) and the magnetic field amplitude are related by the speed of light (\(c\)):\[ B_0 = \frac{E_0}{c} \] Using the given electric field amplitude of \(5.40 \times 10^{-2}\) V/m, we calculated the magnetic field amplitude to be approximately \(1.80 \times 10^{-10}\) T. This relationship is fundamental in understanding the interplay between electric and magnetic components in waves.

Intensity (\(I\)) is a measure of power per unit area carried by a wave. It's a crucial quantity in understanding how much energy a wave transfers through a certain area over time.For electromagnetic waves, intensity is computed using the formula:\[ I = \frac{1}{2} c \varepsilon_0 E_0^2 \] Here, \(\varepsilon_0\) is the permittivity of free space, with a value of \(8.85 \times 10^{-12} \mathrm{F/m}\). Using our electric field amplitude and speed of light, the wave intensity was calculated as approximately \(0.38 \mathrm{W/m^2}\). Understanding intensity helps us grasp how waves can affect materials they encounter, making it an important concept across various scientific and practical applications.