# The electric field of a sinusoidal electromagnetic wave obeys the equation E = - 375 (V/m)sin...

## Question:

The electric field of a sinusoidal electromagnetic wave obeys the equation {eq}E = - 375\ (V/m)sin ((5.97 \times 10^{15}\ (rad/s)) t + (1.99 \times 10^7\ (rad/m)) x). {/eq}

a. What is the amplitude of the electric field of this wave?

b. What is the amplitude of the magnetic field of this wave?

c. What is the frequency of the wave?

d. What is the wavelength of the wave?

e. What is the period of the wave?

f. What is the speed of the wave?

## Electromagnetic Wave

An electromagnetic wave is a transverse wave and it does not require a medium for its propagation. It is a nonmechanical wave. An electromagnetic wave consists of mutually perpendicular electric field oscillations and magnetic field oscillations. In an electromagnetic wave, the mutually perpendicular electric field oscillations and magnetic field oscillations can be in any direction perpendicular to the direction of propagation. An electromagnetic wave can be represented by a periodic function.

• Electric field and magnetic field oscillations in an electromagnetic wave propagating in the x direction can be represented as {eq}E_y = E_0 \sin ( \omega t - k x ) \\ B_z = B_0 \sin ( \omega t - k x ) {/eq} In this equation {eq}E_0, \ \ B_0, \ \ \omega, \ \ k, \ \ t {/eq} are the electric field amplitude, magnetic field amplitude, angular frequency, wave vector and time respectively.
• In an electromagnetic wave electric field amplitude and magnetic field amplitude are related by the equation {eq}\dfrac { E_0} { B_0} = c {/eq}. Here c is the speed of light in vacuum or the speed with which electromagnetic wave propagate in vacuum.