d) If the frequency of this EM wave is 10¹0 Hz, figure out the electric and magnetic field vectors as a function of time and space at this distance. (Write E along y, and B along z direction.) e) Write the Poynting vector for this EM wave.
Electromagnetic Power Density
The power density of an electromagnetic (EM) wave is proportional to the square of the frequency of electric field (or magnetic field). The moving charge produces both electric field and magnetic field. Electric and magnetic fields are inseparable and exist in combination in EM waves.
Wave Reflection and Transmission
Reflection is defined as a sudden change in the path of the wave that strikes the boundary between two types of media. The least part of the disturbances coming from the wavelength remains the same within the same area. The reflection of the wave takes place by following everyday thinking, simple rules, at the ends of the plane. The coefficient of reflection is the ratio of the amplitude of the reflected wave to the value of the incident wave.
Skin Depth
The wire-type conductors are used in the transmission of electrical energy or signals using an alternating current. The electrons are driven apart due to the electric field created nearby the copper conductor surface. The magnetic field changes with the change in the current density. This change in the magnetic field produces an electric field that opposes the current density change. This electric field is known as back electromotive force (EMF). This force is stronger inside the copper conductor and is weaker at the surface. An alternating current can be induced due to the magnetic field according to the law of induction. Such a current is produced due to the electromagnetic wave impinging on the copper conductor.
Plane wave propagation
Any of the ways how waves travel is known as wave propagation. One can find the difference between longitudinal wave and transverse wave with respect to the direction of oscillation, which is related to the propagation direction. Propagation may occur in vacuum for electromagnetic waves as well as in material medium. Other types of waves need a transmission medium to exist and cannot propagate through the vacuum. The amplitude of a wave is the maximum distance from the displacement of the particle from its resting position on the medium. The waves that propagate are of two types, Pressure waves or Shear waves.
Help with d & e
![5. A radio station is radiating EM waves with an average power of Pave = 1500 kW from its vertical antenna whose
length is L = 10 m. Assume that the radiation is spherically symmetric around this antenna.
a) What is the average intensity of the laser light at a distance of 12.2 km from the source point?
b) What is the radiation presure of the laser light at this distance on a totally reflective surface?
c) What are the maximum values of the electric and magnetic fields at this distance?
d)
If the frequency of this EM wave is 10¹0 Hz, figure out the electric and magnetic field vectors as a function
of time and space at this distance. (Write E along y, and B along z direction.)
e)
Write the Poynting vector for this EM wave.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F51435bf2-32bb-499c-aa57-a85dc35bd95d%2Fe3290271-de76-4e62-acc7-ae9b0f2c23f7%2Finl4y85_processed.jpeg&w=3840&q=75)
![(9) We know that Average intensity is the measure of average
power per unit Area
Iavy
Pary
A
where
Iavy
and
=
=
2
Emax
(b) We know that the Radiation pressure on
given by
PR =
(1+x) Iavg
=
x = reflection
PR =
= 8x10-4 Wm-2
0.80 X 10-3 Wm-²2
Parg =
чля2
2 Iavy
с
2 Javg
CEO
Bmax.:
=
1500 X 10³ W
47 (12-2x10³m) 2
(c) we know that average intensity can be written as
Tavg
= CEo Emax
2
с
coefficient = 1 (for totally Reflecting surface)
Emaa
с
any
2X 8 X 10-4 Wm 2
3х108 mis
2x8x104
3X108 x8-854x10-12
surface is
=
=
Emax. = 0.775 X104 v/m = 7075 x10³ V/m
7.75X103
3x108
= 5.33 X10-¹² Nm ²²
0.602x10² √²/m²
2.58×105T](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F51435bf2-32bb-499c-aa57-a85dc35bd95d%2Fe3290271-de76-4e62-acc7-ae9b0f2c23f7%2Ft78eyeb_processed.jpeg&w=3840&q=75)
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