Question

The electric field associated with a uniform plane wave propagating in free space is described by ( E = 50e ) V/m. Find the following:

(a) Direction (polarization) of

electric field.
(b) Direction in which the wave travels.
(c) Wavelength.
(d) Frequency and period.
(e) Magnetic field vector.
(f) Real-time form of electric field.
a) ( E = 50e ) V/m; Propagation direction = ( -y ); Wavelength = ( lambda ); Frequency = ( clambda ); Magnetic field = ( B = Ec ); ( E = 50ecos(Ω t - kz) )
b) ( E = 50e ) V/m; Propagation direction = ( x ); Wavelength = ( cf ); Frequency = ( f ); Magnetic field = ( B = Ec ); ( E = 50esin(Ω t - kz) )
c) ( E = 50e ) V/m; Propagation direction = ( z ); Wavelength = ( cf ); Frequency = ( clambda ); Magnetic field = ( B = Ec ); ( E = 50ecos(Ω t + kz) )
d) ( E = 50e ) V/m; Propagation direction = ( y ); Wavelength = ( lambda ); Frequency = ( f ); Magnetic field = ( B = Ec ); ( E = 50esin(Ω t + kz) )

Answer 1

The direction of a plane electromagnetic wave's electric field defines its polarization, while the wave itself travels perpendicular to both the electric and magnetic fields. Wavelength and frequency are inversely related as per the equation λ=c/f. The magnetic field is perpendicular to the electric field and is found using the relation B=E/c.

Step-by-step explanation:

In classical electromagnetism, a plane electromagnetic wave is a wave solution of the Maxwell's equations that describes the propagation of light and other forms of electromagnetic radiation.

• The direction of the electric field vector (E) defines the polarization.
• The wave propagates in a direction that is perpendicular to both the electric and magnetic fields.
• The wavelength (λ) is the distance over which the wave's shape repeats, and it is inversely proportional to the frequency when multiplied by the speed of light (λ=c/f).
• The frequency (f) is the number of cycles of the wave that pass a fixed point in unit time, and the period (T) is the reciprocal of the frequency (T=1/f).
• The magnetic field vector (B) is perpendicular to the electric field and is obtained from the electric field using the relation B=E/c, where c is the speed of light.
• In terms of real-time representation, electric and magnetic fields oscillate sinusoidally with time and space, typically expressed using cosine or sine functions.

The intensity of an electromagnetic wave with a peak electric field strength can be calculated using the equation I=(E^2)/(2cμ₀), where E is the electric field amplitude, and μ₀ is the permeability of free space. The Poynting vector represents the directional energy flux (the rate of energy transfer per unit area) of an electromagnetic field.