Electromagnetic Waves as Sinusoidal Waves Video Lessons

Concept

# Problem: In SI units, the electric field in an electromagnetic wave is described by Ey = 102 sin(1.40 107x − ωt).(a) Find the amplitude of the corresponding magnetic field oscillations.(b) Find the wavelength λ.(c) Find the frequency f.

###### FREE Expert Solution

The form of a plane wave solution for an electric field is:

$\overline{){\mathbf{E}}{\mathbf{=}}{{\mathbf{E}}}_{{\mathbf{0}}}{\mathbf{s}}{\mathbf{i}}{\mathbf{n}}{\mathbf{\left(}}{\mathbf{k}}{\mathbf{x}}{\mathbf{-}}{\mathbf{\omega }}{\mathbf{t}}{\mathbf{\right)}}}$

ω is the angular frequency and t is the time for the oscillations.

The electromagnetic wave described above is Ey = 102 sin(1.40 107x − ωt)

(a)

The amplitude of the corresponding magnetic field is expressed as:

$\overline{){{\mathbf{B}}}_{{\mathbf{0}}}{\mathbf{=}}\frac{{\mathbf{E}}_{\mathbf{0}}}{\mathbf{c}}}$, where E0 is the amplitude of electric field and c is the speed of electromagnetic wave given as 3.0 × 108 m/s.

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###### Problem Details

In SI units, the electric field in an electromagnetic wave is described by Ey = 102 sin(1.40 107x − ωt).

(a) Find the amplitude of the corresponding magnetic field oscillations.

(b) Find the wavelength λ.

(c) Find the frequency f.