### PHYS2210 Electromagnetism

• Level 2 Physics course
• Units of Credit (UOC): 6
• Offered every year, Session 2

#### Lecturers:

ELECTROMAGNETISM

Brief Syllabus:

• Vector analysis
• Electrostatic field, electric potential; work and energy in electrostatics
• Electrostatic fields in matter; polarization, displacement, dielectrics
• Current electricity; electric current, current density, continuity equation, Drude's model of a conductor, Ohm's Law, Kirchhoff's Laws
• Magnetostatics; magnetic fields, Lorentz force law, Biot-Savart law, Ampère’s law
• Magnetostatic fields in matter; diamagnetism, paramagnetism, ferromagnetism
• Electrodynamics
• Maxwell’s equations

Assumed Knowledge:
The course assumes familiarity with first year physics, e.g. PHYS1221 or PHYS1231 or PHYS1241 and second year mathematics MATH2011 or MATH2111.

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Course Goals:
Electromagnetism is important from both fundamental and applied viewpoints. This course aims to provide students with an introduction to the principles and behaviour of electric and magnetic systems. The course begins by considering the electric effects of static electric charge distributions. Then, we consider magnetic effects (i.e. what happens when you allow the electric charges to move). Finally, we combine both the electric and magnetic behaviours into a unified topic Electromagnetism and introduce Maxwell’s four equations which provide an elegant summary of this subject. We will also see that there are two, equivalent mathematical descriptions of Electromagnetism i.e differential and integral.

Specific topics include:

• An introduction to the mathematical methods of vector analysis (div, grad and curl) used to describe electromagnetic quantities such as field and potential.
• The effects of static electric charge distributions. Electric fields. Gauss’ law.
• The response of real materials to applied electric fields; dielectrics. Electric polarization and displacement. The fundamental electric vectors E, D and P.
• The magnetic fields due to electric currents. Calculation of magnetic fields, Biot-Savart and Ampère laws.
• The response of real materials to magnetic fields; types of magnetism of real materials, diamagnets, paramagnets, ferromagnets. The fundamental magnetic vectors B, H and M.
• Induced EMF due to changing magnetic flux; Faraday and Lenz laws.
• Maxwell’s equations

Learning Objectives

• Students will gain an appreciation of how the topics of Electricity and Magnetism are related and unified.
• Students will be introduced to Maxwell’s equations which encompass the work of Gauss, Ampère and Faraday.
• Hopefully the student will gain an appreciation of why Maxwell’s equations are often referred to as the crowning glory of 19th century science.

Why is Electromagnetism important?

Electromagnetism underpins the operation of much of today’s technology (e.g. radio, TV, computers, data storage, radar, microwave ovens, motors, MRI, …). From a fundamental perspective, it is one of the four ‘types’ of force found in nature and Maxwell’s ‘discovery’ that light is an electromagnetic wave ranks as one of the greatest breakthroughs in science. Furthermore, Einstein was led to his formulation of the theory of relativity by the in-depth study of Maxwell’s work. To quote J.R. Pierce, “To anyone who is motivated by anything beyond the most narrowly practical, it is worthwhile to understand Maxwell’s equations simply for the good of his soul”.

The course is strongly recommended as groundwork for a number of 3rd year courses such as PHYS3011 Quantum Mechanics and Electrodynamics.

How to succeed - Strategies for Learning

Some students find this subject confusing and, in many cases, this is due to the use of vector analytical techniques involving div, grad and curl. It is important that you gain some familiarity with these techniques of differential calculus by doing problems.

Like most subjects, the key to success is hard work. A number of tutorial sheets covering the entire course will be available on the Web. The student should work through these problems bit by bit, (alone or with a group), to keep pace with the lectures. In this way the student can get the practice and experience necessary to understand the physical phenomena and mathematical techniques presented here. Solutions to specific problems will be discussed during lectures, as appropriate.

The material discussed in lectures will follow the textbook closely and it is very useful, as in any course, for the student to prepare a concise summary of the material presented in lectures. Don’t just memorise all the equations (a formula sheet will be attached to the exam paper) - concentrate on the physics.

Assessment

2 hour written examination 60%
Two assignments 10% each
Mid session test 20%

For rules regarding academic honesty, etc, see the School website here.

Resources:

Textbook

David J. Griffiths, Introduction to Electrodynamics, 3rd edition (Prentice Hall). (You might find copies of the 2nd edition available; this is also a suitable textbook for this course).

It is always a good idea to consult more than one book when studying a course as you may find a book whose particular style is more suited to yours than the prescribed textbook. You will also benefit from studying different approaches to the course material and related problems; here is a short list of books which might be useful:

P. Lorrain and D.R. Corson, Electromagnetic fields and waves.
J.D. Jackson, Classical Electrodynamics (Wiley).
H.M. Schey, Div, Grad, Curl and all that (Norton) – vector analysis.
E.M. Purcell, Electricity and Magnetism (McGraw-Hill)
B. and B.I. Bleaney, Electricity and Magnetism (Oxford) – an old classic.

Information on student support services may be found on the School here.

Detailed Syllabus

 TOPIC TEXT REFERENCE Vectors Scalars, vectors and their products. Div, Grad and Curl. Line, surface and volume integrals. Gradient, Divergence and Stokes’ theorems. Curvilinear coordinates, Dirac delta function, vector fields. 1.1 - 1.6 The Electrostatic Field Coulomb’s law. Electric field (E). Charge distributions, Gauss’ law. Div and Curl of E. Electric potential. Poisson’s equation. Energy stored in a charge distribution. Conductors. 2.1 – 2.5 Special Techniques Multipole expansion 3.4 Dielectrics Polarization (P), dipoles, bound charge density. Electric displacement (D). Electric susceptibility and permittivity. Boundary conditions. Dielectric materials in an E field. 4.1 – 4.4 Current electricity Electric current, current density, continuity equation, Drude's model of a conductor, Ohm's Law, Kirchhoff's Laws 7.1.1 and 8.1.1 Magnetostatics Lorentz force law. The magnetic field (H) and magnetic induction (B). Biot-Savart law. Ampère’s law. Div and Curl of B. Maxwell’s equations for static fields. Magnetic vector potential. 5.1 – 5.4 Magnetization Magnetic torque and force. Hall effect. Magnetic dipoles and Magnetization (M). Bound currents. Magnetic field of a magnetized object. Magnetic materials (diamagnetism, paramagnetism, ferromagnetism, hysteresis, domains, superconductors). 6.1 – 6.4 Magnetic Induction EMF. Faraday’s law. Lenz’s law. Mutual Inductance, Self Inducatance. 7.1 – 7.2 Maxwell’s Equations Ampère’s law revised. Maxwell’s equations inside matter. Electromagnetic waves and the Poynting vector. 7.3; 8.1

last updated 29 July 2013