A plane electromagnetic wave propagates in a vacuum in the z-direction. The wave has a wavelength of 10 m and the electric field is along the +x direction and has an amplitude of is 0.20 V/m, with one maximum at x = 0 and t = 0. What is the mathematical expression for the magnetic field? A)B_y = 0.067 × 10^-8sin[(0.63 m^-1)z - (2.1 × 10^-9 s^-1)t] T B)B_y = 0.067 × 10^-8sin[(0.63 m^-1)z + (2.1 × 10^-9 s^-1)t] T C)B_y = 0.067 × 10^-8cos[(0.63 m^-1)z + (1.9 × 10⁸ s^-1)t] T D)B_y = 0.067 × 10^-8cos[(10 m^-1)z - (2.1 × 10^-9 s^-1)t] T E)B_y = 0.067 × 10^-8cos[(0.63 m^-1)z - (1.9 × 10^-8 s^-1)t] T

Question

Quizplus · Accepted Answer

The magnetic field is perpendicular to both the electric field and the direction of propagation. The amplitude of the magnetic field is given by B = E/c, where c is the speed of light. The wave number k = 2π/λ = 0.63 m⁻¹ and the angular frequency ω = 2πf = 1.9 × 10⁸ s⁻¹. The correct expression is a cosine function with the correct wave number and angular frequency.

A Plane Electromagnetic Wave Propagates in a Vacuum in the Z-Direction