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Juan Pablo Diaz Diaz Group 203058_20 CC: 1095791511

UNIVERSIDAD NACIONAL ABIERTA Y A DISTANCIA UNAD Escuela de Ciencias Básicas, Tecnología e Ingeniería Teoría Electromagnética y Ondas 2019

Introduction Inside this document you will find the principle definitions of an electromagnetic wave and its principle characteristics like permittivity and permeability

Solution of the 5 questions 1. What is an electromagnetic wave? Electromagnetic waves or EM waves are waves that are created as a result of vibrations between an electric field and a magnetic field. In other words, EM waves are composed of oscillating magnetic and electric fields. Electromagnetic waves are formed when an electric field comes in contact with a magnetic field. They are hence known as ‘electromagnetic’ waves. The electric field and magnetic field of an electromagnetic wave are perpendicular (at right angles) to each other. They are also perpendicular to the direction of the EM wave. EM waves travel with a constant velocity of 3.00 x 108 ms-1 in vacuum. They are deflected neither by the electric field, nor by the magnetic field. However, they are capable of showing interference or diffraction. An electromagnetic wave can travel through anything - be it air, a solid material or vacuum. It does not need a medium to propagate or travel from one place to another. Mechanical waves (like sound waves or water waves), on the other hand, need a medium to travel. EM waves are 'transverse' waves. This means that they are measured by their amplitude (height) and wavelength (distance between the highest/lowest points of two consecutive waves). The highest point of a wave is known as 'crest', whereas the lowest point is known as 'trough'. Electromagnetic waves can be split into a range of frequencies. This is known as the electromagnetic spectrum. Examples of EM waves are radio waves, microwaves, infrared waves, X-rays, gamma rays, etc. 2. What is electrical permittivity 𝜺 and magnetic permeability 𝝁 of a medium? Permittivity is analogous to the Conductivity of a conductor, similar to the conductivity which is the property of a material by which it allows free flow of electrons through it, Permittivity is the property of a material by which it allows the free flow of electric field through it. permittivity describes the amount of charge needed to generate one unit of electric flux in a given medium. A charge will yield more electric flux in a medium with low permittivity than in a medium with high permittivity. Permittivity is the measure of a material's ability to store an electric field in the polarization of the medium. 𝜺

Permittivity = 𝜺𝒓 = 𝜺

𝟎

Magnetic permeability (μ) is the ability of a magnetic material to support magnetic field development. In other words, magnetic permeability is the constant in the proportionality between magnetic induction and magnetic field intensity. The greater the magnetic permeability of the material, the greater the conductivity for magnetic lines of force, and vice versa. The magnetic permeability of a material indicates the ease with which an external magnetic field can create a higher magnetic force of attraction in the material. The SI unit of magnetic permeability is Henry per meter. 3. In a vacuum, what is the value of the electric permittivity 𝜺𝒐 and the magnetic permeability 𝝁𝒐 ? 

The Permittivity of Vacuum is denoted by 𝜀0 and is equal to: 8.854𝑥10−12 .



the magnetic permeability of vacuum is denoted by 𝜇𝑜 and is equal to:1.25663706212(19)𝑥10−6 H/m

4. If the relationship between relative and absolute electric permittivity in a medium is 𝜺 = 𝜺𝒓 𝜺𝒐 , what is for the absolute magnetic permeability 𝝁 and the relative 𝝁𝒓 ? The absolute permeability of another material can be expressed relative to the permeability of free space. Then, 𝝁 = 𝝁𝟎 𝝁𝒓 Where 𝜇𝑟 is the dimensionless quantity called relative permeability. 2𝜋

5. In the wave equation 𝐸(𝑥, 𝑡) = 𝐴 𝑠𝑒𝑛(𝑘𝑥 − 𝑤𝑡)𝑗̂ = 𝐴 𝑠𝑒𝑛 ( 𝜆 𝑥 − 2𝜋𝑓𝑡) 𝑗̂ identify the following parameters and their unit: - Amplitude: _A_ [m] (example). 𝟏

- Frequency: 𝑻 [Hz] - Weather: ___ - Angular frequency: 𝝎 = 𝟐𝝅𝒇 [𝑯𝒛] - Wavelength: - Wave number: 𝒌 =

𝟐𝝅 𝝀

[measured in cycles per unit distance or radians per unit distance]

- Polarization direction: linear - Direction of displacement: ___ Conclusions Conclusion 1: Permittivity and permeability are two different measures used in electromagnetism. Permittivity measures the ability of a material to store energy within the material. Permeability, on the other hand, is a measure of the

ability of a material to support the formation of a magnetic field within the material. The permittivity of a material is related to the polarization of the material whereas the permeability of a material related to the magnetization of the material. This is the main difference between permittivity and permeability. Permittivity and permeability have very different and particular meanings in electromagnetism. Conclusion 2: Electromagnetic waves are preset in our daily live and they are very helpful, in the electromagnetic spectrum we have different type of waves (radio and microwave, infrared, visible light, ultraviolet and X-ray/gamaray) each one with different length of wave and different function.

Bibliography   

Quesada, M., & Maroto, J. (2014). Plane electromagnetic waves. Electromagnetic waves in free space. From Maxwell's Equations to Free and Guided Electromagnetic Waves: An Introduction for First-year Undergraduates. New York: Nova Science Publishers, Inc. Gutiérrez, W. (2017). Loss Tangent [Video]. Recovered from http://hdl.handle.net/10596/13139 Chen, W. (2005). The Electrical Engineering Handbook. Boston: Academic Press.