Final answer:
The question involves finding amplitude, frequency, wavelength, direction of travel, and associated magnetic field wave of an electromagnetic wave represented by the equation E(z,t) = 50cos(2π×10⁹t−kz)(V/m). Amplitude is 50 V/m, frequency is 1 GHz and direction of travel is in the positive z direction. the associated magnetic field can be determined using Maxwell's equations.
Step-by-step explanation:
The student is asking about specific quantities related to an electromagnetic wave equation in air, which has been given as E(z,t) = 50cos(2π×10⁹t−kz)(V/m). They want to sketch the waveforms for E(t) versus t at a given position z in terms of the wavelength λ.
The quantities to be found are:
- Amplitude (A): This is the maximum value of the electric field strength, which can be read directly from the equation as 50 V/m.
- Frequency (f): This is the number of oscillations the wave makes per second and is associated with the 2π×10⁹t term in the equation, giving it a value of 10⁹ Hz or 1 GHz.
- Wavelength (λ): Wavelength is the distance over which the wave's shape repeats and is related to the wavenumber k in the equation, where k = 2π/λ.
- Direction of travel: The direction of travel is indicated by the negative sign before kz, meaning that the wave is traveling in the positive z direction.
- The associated magnetic field wave can be found using Maxwell's equations, which state that the electric and magnetic fields are perpendicular to each other and to the direction of wave propagation in an electromagnetic wave.