PHY4XRY - Physics of Electromagnetism: Assignment 2 Solution

This document presents a comprehensive solution to PHY4XRY Assignment 2, focusing on the fundamental principles of electromagnetism. It begins by discussing the physical meaning of each term within the equations 𝐷⃗ = 𝜀0𝐸⃗ + 𝑃⃗ and 𝐻⃗ = 𝐵⃗ /𝜇0 − 𝑀⃗, including electric field, electric displacement, auxiliary field, magnetic flux density, permeability of free space, magnetism, permittivity of free space, and polarization. The solution then delves into Gauss's law and Ampere's law, explaining their significance and applications in electromagnetism. The assignment also includes a derivation, starting from Maxwell's equations for a homogeneous, linear, isotropic, dielectric material, to show a specific electromagnetic relationship, with clear explanations of all assumptions made. The document concludes with a list of references used for the solution.

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Question 1:
a) Discuss the physical meaning of each term in the following relations
𝐷⃗ = 𝜀0𝐸⃗ + 𝑃⃗
𝐻⃗ = 𝐵⃗ /𝜇0 − 𝑀⃗
E = Electric field
Electrical field refers to region around a charged object or particles within a force would be
exerted on other charged objects or particles.
D = Electric displacement
Electric displacement, also known as electrical flux density, it refers as the charge per unit area,
which can be displaced across a layer of conductors placed across an electric filed (Fushchich &
Nikitin 2013).
H = Auxiliary field
Is one whose equations of motion admit a single solution (Kaminer et al 2012).
B = Magnetic flux density
Flux density refers to the measure of the number of magnetic lines of force per unit of cross-
sectional area (.
𝜇0 permeability of free space
The permeability of free space, μ0, is a physical constant used often in electromagnetism. It is
defined to have the exact value of 4π x 10-7 N/A2
M= Magnetism
Magnetism is a class of physical phenomena which are initiated by the magnetic fields.
𝜀0 Permittivity of free space

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Is a concept, physical constant, which is the value of the absolute dielectric
permittivity of classical vacuum.
P= Polarization
Polarization refers to the vector field that shows the density of induced or permanent magnetic
dipole moments in a magnetic material (Huray 2011).
b) Discuss Gauss’ law and Ampere’s law
i) Gauss’ law
The electric flux of the gauss’ law is the electric field fleeting through a specified area multiplied
by the surface area in a plane that is at the right angle to the field. The net flux of a particular
electric field through a given surface, divided by the charge enclosed should be the same as a
constant (Shin & Fan 2012).
Normally, electric charge that is positive is supposed to create an electric field that is positive.
The net flux of an electric field in a surface that is in a closed surface is directly proportional to
the electric charge that is enclosed.
ii) Ampere’s law
The space magnetic field around the electric current is proportional to the electric current which
functions as its source, just like the electric field in the space is proportional to the charge that
functions as the source (Kirsch & Hettlich 2016). . The law states that for every closed loop path,
the total amount of the length elements multiplied with the magnetic field in the length element
direction which is equal to the permeability multiplied by the electric current bounded in the
ring.
Question 2

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Assumptions made
1. Medium 𝜀 and μ are independent of position,
2. μo and 𝜀0 are constant in time
3. isotropic media 𝜀 and μ are time independent scalars
Question 3

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Question 4

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Question 5

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References
Fushchich, W. I., & Nikitin, A. G. (2013). Symmetries of Maxwell’s equations (Vol. 8). Springer Science &
Business Media.
Huray, P. G. (2011). Maxwell's equations. John Wiley & Sons.
Kaminer, I., Bekenstein, R., Nemirovsky, J., & Segev, M. (2012). Nondiffracting accelerating wave
packets of Maxwell’s equations. Physical review letters, 108(16), 163901.
Kirsch, A., & Hettlich, F. (2016). Mathematical Theory of Time-harmonic Maxwell's Equations. Springer
International Pu.
Shin, W., & Fan, S. (2012). Choice of the perfectly matched layer boundary condition for frequency-
domain Maxwell’s equations solvers. Journal of Computational Physics, 231(8), 3406-3431.