Time: 97 hours
College Credit Recommended
Electromagnetism extends our understanding beyond classical mechanics because it introduces the concept of charge – a property we can observe in macroscopic objects and the smallest building blocks of matter. Electromagnetism is the invisible hand that allows charged objects to interact with each other. It also allows you to take this course: the modern world would be impossible without telecommunications and microelectronics, two of the major applications of electromagnetism.
Scientists began studying electromagnetism in the 18th century. They prepared the groundwork for developments in the 20th century and our modern understanding of atomic structure and the cosmos. In this course, we will learn why electromagnetism is so important for everyday applications and fundamental physics. To put this information into proper context, you should be familiar with the force concept of classical mechanics.
Building on the idea of force, we develop the more abstract concept of fields. This study culminates in Maxwell's theory which, among other achievements, led to the discovery of radio waves. We begin by discussing waves and oscillations in the more familiar setting of mechanics to review how forces relate to the motion of objects. This preparation will help you understand Maxwell's insights into the nature of electromagnetic radiation as a wave phenomenon.
The term "electromagnetism" combines two effects we will study separately: electricity and magnetism. We explore electrical measurements and circuits to learn how to observe, quantify, and apply the laws that govern how charges cause static electricity and magnetism. In Maxwell's equations, we will finally unify electric and magnetic effects and discover electromagnetic radiation. This will also put radio waves on the same footing as light: they are the same phenomenon, differing only in their wavelength.
In the final units of this course, we look at optics and Einstein's theory of special relativity. You can think of optics, the science of light, as a practical application of electromagnetism. However, the theory of relativity is an entirely new way of looking at the nature of space and time. This paradigm shift in the foundations of physics was inspired directly by the discoveries at the heart of this course.
First, read the course syllabus. Then, enroll in the course by clicking "Enroll me in this course". Click Unit 1 to read its introduction and learning outcomes. You will then see the learning materials and instructions on how to use them.
This unit is a review of the mathematical background necessary to solve many problems in the study of electromagnetism. You may wish to refer to it as necessary as you work through the rest of the course.
If you already feel comfortable with these topics, you may skip this unit. This unit is not required to complete this course.
The material in this unit is not directly related to electricity and magnetism, but it is the foundation of one of the most significant outcomes of Maxwell's theory – electromagnetic waves. In PHYS101: Introduction to Mechanics, we learned how to describe the motion of particle-like masses using classical mechanics. In this unit, we begin the transition from mechanics to electromagnetism by examining how objects of size – length, width, and depth – behave.
When we look at these types of extended objects, a mystery is hiding in plain sight: if you pull one end of a rope, how does the other end know? Your action somehow "propagates" from one end to the other. The answer is related to the invisible hand of electromagnetism that can transmit information between different locations.
In this unit, we focus on vibrating systems and the propagation of mechanical waves through media; think of ripples traveling outward from a stone dropped into water. We also lay the basic foundation for the development of a classical theory of mechanics for extended solids.
Completing this unit should take you approximately 7 hours.
Now, let's turn to the study of electricity and magnetism, two different aspects of electromagnetism. We start by looking at electrostatics: the rules that govern the behavior of static charges. Thales of Miletus (c. 624–548 bc), the Greek mathematician, astronomer, and philosopher, carried out the first experiments on electrical phenomena when he observed that you can generate a static charge when you rub amber with wool.
Completing this unit should take you approximately 20 hours.
Although the study of electric and magnetic fields is interesting in and of itself, it may not seem directly useful in the real world. However, the interplay between these phenomena is responsible for much of the technology you see in your everyday life. For example, all electronics apply various features of electromagnetism, so that computers, HDTV, iMacs and iPads, smartphones, motors, fans, lights, and so on are applied electromagnetic devices. In this unit, we will take a quick look at the foundations of electronics while at the same time adding to our understanding of electromagnetism.
Completing this unit should take you approximately 8 hours.
Now that we have studied electric charges, potentials, and fields, let's look at the effect of moving charges: magnetism. Thales of Miletus set the stage for the scientific exploration of magnetism back in Ancient Greece, when he could only observe magnetism via the behavior of natural magnets, called lodestones.
Hans Christian Oersted documented the relationship between moving electric charges and magnetism much later, in 1820 when he accidentally discovered that an electric current could deflect a nearby compass needle. James Clerk Maxwell united electrical and magnetic phenomena into four reasonably simple equations, which we know as Maxwell's Equations, 45 years after Oersted made his observation.
The discovery that electrical currents cause magnetic effects led to the invention of the galvanometer, which we have already encountered as the core component of ammeters and voltmeters.
Completing this unit should take you approximately 7 hours.
We have learned that stationary electric charges produce an electric field, and that moving electric charges (electric current) produce a magnetic field. In this unit, we discover that the reverse is also true: changing magnetic fields can produce an electric field, or induce an electric current. This describes the phenomenon of electromagnetic induction, a basic principle that drives electric power generators and transformers.
Completing this unit should take you approximately 13 hours.
Maxwell's four equations describe classical electromagnetism. James Clerk Maxwell, (1831–1879), the Scotish physicist, first published his classical theory of electromagnetism in his textbook, A Treatise on Electricity and Magnetism in 1873. His description of electromagnetism, which demonstrated that electricity and magnetism are different aspects of a unified electromagnetic field, holds true today. In fact, Maxwell's equations are consistent with relativity, which was not theorized until 30 years after he had completed his equations.
Completing this unit should take you approximately 8 hours.
An optical phenomenon involves an interaction between electromagnetic waves and matter. The complete study of optics involves complex mathematics, a thorough understanding of both classical and quantum optical effects, and a great deal of engineering.
We begin by applying simplified models to develop a basic understanding of how optics works, without having to remember all of Maxwell's equations. In geometric optics, we ignore all the effects that are germane to waves, such as interference. This will nevertheless allow us to understand a large variety of phenomena. We will return to the complexities of wave physics as related to optics in the section on wave optics at the end of this unit.
Completing this unit should take you approximately 11 hours.
The physical descriptions we have studied to this point were based on a notion of absolute space and time. A model for this point of view was that space is filled everywhere by a continuous medium called the ether. Light and other forms of electromagnetic radiation were waves in this ether, analogous to sound waves in air. All other phenomena were to be understood as various manifestations of Maxwell's electromagnetism, which was originally based on a mechanical model of ether. It seemed reasonable that the 19th Century "theory of everything" could be tied down by measuring the "elastic" properties of the ether.
Toward the end of the 1800s, however, this model became associated with more and more hastily patched cracks. The detailed history of the gradual realization that ether models were not quite right is complex and technical. However, there is one rather clear indication of trouble. In 1887, Albert Michelson and Edmund Morley of the Case Institute (now Case Western University) performed an experiment using an optical interferometer in which they compared the speed of light in two beams traveling at right angles to each other. If the speed of light relative to the ether was always the same, the measured speed of light would be larger or smaller depending on the direction the experiment was traveling through the ether. The motion of the Michelson-Morley experiment was provided by the rotation of the Earth on its axis and the orbital motion of the Earth around the Sun, as well as the absolute velocity (if any) of the Sun relative to the ether.
They expected to see both diurnal changes and yearly changes in the relative velocities of light in the two paths. True, the changes expected by classical ether theory were small (on the order of 0.01% of the velocity of light), but the Michelson-Morley interferometer was able to detect velocity changes about 6-7 times smaller. To the surprise of all, there were no changes whatsoever observed. This experiment was widely repeated, using constantly improving equipment – a new version of the experiment carried out in 2002 established that the velocity of light is constant to better than 1 part in 1015 – one of the most precise physical measurements ever accomplished.
The explanation of the Michelson-Morley null result was length contraction, as developed by Hendrik Lorentz and George Francis FitzGerald. Length contraction explained the Michelson-Morley result, the idea being that matter is held together by electromagnetic forces (true), and so the actual size of objects will change with motion through the ether (false). In the end, it was Albert Einstein's formulation of the theory of Special Relativity that gave us a consistent explanation of all such phenomena. His primary postulate was to accept that the speed of light and the laws of physics are constant in all reference frames – including reference frames that are in motion. Oddly, despite the fact that Einstein's theory completely explained the Michelson-Morley result, he took no motivation for his theory from that experiment.
Completing this unit should take you approximately 10 hours.
This study guide will help you get ready for the final exam. It discusses the key topics in each unit, walks through the learning outcomes, and lists important vocabulary. It is not meant to replace the course materials!
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Certificate Final Exam
Take this exam if you want to earn a free Course Completion Certificate.
To receive a free Course Completion Certificate, you will need to earn a grade of 70% or higher on this final exam. Your grade for the exam will be calculated as soon as you complete it. If you do not pass the exam on your first try, you can take it again as many times as you want, with a 7-day waiting period between each attempt.
Once you pass this final exam, you will be awarded a free Course Completion Certificate.
Saylor Direct Credit
Take this exam if you want to earn college credit for this course. This course is eligible for college credit through Saylor Academy's Saylor Direct Credit Program.
The Saylor Direct Credit Final Exam requires a proctor and a proctoring fee of $25. To pass this course and earn a Proctor-Verified Course Certificate and official transcript, you will need to earn a grade of 70% or higher on the Saylor Direct Credit Final Exam. Your grade for this exam will be calculated as soon as you complete it. If you do not pass the exam on your first try, you can take it again a maximum of 3 times, with a 14-day waiting period between each attempt.
Once you pass this final exam, you will be awarded a Credit-Recommended Course Completion Certificate and an official transcript.