Light and Optics

# Light and Electromagnetism

by Nathaniel Page Stites, M.A./M.S.

In 1873, seventy years after Thomas Young presented his experimental results on the nature of light (see our Light I: Particle or Wave? module), a Scottish physicist named James Clerk Maxwell published a theory that accounted for the physical origins of light. Throughout the nineteenth century, many of science's greatest minds dedicated themselves to the study of two exciting new ideas: electricity and magnetism. Maxwell's work synthesized these two ideas, which had previously been considered separate phenomena. His new theory was aptly named a theory of electromagnetism.

## Early experiments in electricity and magnetism

The earliest experimental connection between electricity and magnetism came in the 1820s from the work of the Danish physicist Hans Christian Oersted. Oersted discovered that a wire carrying electric current could deflect the needle of a magnetic compass. This planted the seed for Andre Ampere, a French physicist, to demonstrate that two current-carrying wires would interact with each other due to the magnetic field that they generated. Ampere found that two long, straight wires carrying current in the same direction would attract each other, and two wires carrying current in opposite directions would repel each other (click on the Interactive Animation links for a demonstration). Ultimately, Ampere formulated a general expression – called Ampere's Law – for determining the magnetic field created by any distribution of electric currents.

Ampere's important contributions to magnetism and electricity led other scientists to conduct experiments that probed the relationship between these two cutting-edge areas of nineteenth century physics. For example, in 1831, Michael Faraday discovered that a change in the magnetic field passing through a loop of wire creates a current in the wire (see the next Interactive Animation). Faraday, an English physicist with almost no formal mathematical training, had observed that passing a bar magnet through a coil of wire created an electric current. Similarly, moving a coil of wire in the vicinity of a stationary magnet also produced electric current. Faraday hypothesized that somehow the magnet "induced" the current in the wire, and named the phenomenon "induction." Faraday's name is still associated with this idea, in the form of "Faraday's Law," which, put simply, says that a changing magnetic field produces an electric field.

Today, the principle behind Faraday's Law is at work in electrical generators. Using some mechanical source of energy (such as a hand crank, a windmill, the force of falling water, or steam from boiling water) to spin a turbine, magnets inside the generator spin next to a large coil of wire. As the magnets spin, the magnetic field that passes through the wire loop changes. This changing "magnetic flux" establishes an "induced" current in the wire and mechanical energy becomes electrical energy. (See the Interactive Animation of a Simple Electric Current Generator.)

Over 40 years after Faraday, James Clerk Maxwell, based on little more than an intuitive feeling for the symmetry of physical laws, speculated that the converse of Faraday's Law must also be true: a changing electric field produces a magnetic field. When Maxwell took the work of Ampere and Faraday and incorporated his new idea, he was able to derive a set of equations (originally there were twenty equations, but now they have been simplified to just four) that completely unified the concepts of electric and magnetic fields into one mathematical model.

Comprehension Checkpoint

Which of the following describes an induced current?

## Electromagnetic waves

After developing his now-famous equations, Maxwell and other physicists began exploring their implications and testing their predictions. One prediction that came from Maxwell's equations was that a charge moving back and forth in a periodic fashion would create an oscillating electric field. This electric field would then set up a periodically changing magnetic field, which in turn would cause the original electric field to continue its oscillation, and so on. This mutual vibration allowed the electric and magnetic fields to travel through space in the form of an "electromagnetic wave," as shown in Figure 1 and the Interactive Animation.

Because this new mathematical model of electromagnetism described a wave, physicists were able to imagine that electromagnetic radiation could take on the properties of waves. Thus, just like all waves, Maxwell's electromagnetic waves could have a range of wavelengths and corresponding frequencies (see our Wave Motion module for more information on waves). This range of wavelengths is now known as the "electromagnetic spectrum." Maxwell's theory also predicted that all of the waves in the spectrum travel at a characteristic speed of approximately 300,000,000 meters per second. Maxwell was able to calculate this speed from his equations:

$$c = 1 ϵ 0 μ 0 = 2.998 × 10 8 m/s$$

where

$$c = speed of the electromagnetic wave$$

$$ϵ 0 = permittivity of free space ( 8.854 × 10 − 12 F/m )$$

$$μ 0 = permeability of free space ( 4 π × 10 − 7 N/ A 2 )$$

Maxwell's calculation of the speed of an electromagnetic wave included two important constants: the permittivity and permeability of free space. The permittivity of free space is also known as the "electric constant" and describes the strength of the electrical force between two charged particles in a vacuum. The permeability of free space is the magnetic analogue of the electric constant. It describes the strength of the magnetic force on an object in a magnetic field. Thus, the speed of an electromagnetic wave comes directly from a fundamental consideration of electricity and magnetism.

When Maxwell calculated this speed, he realized that it was extremely close to the measured value for the speed of light, which had been known for centuries from detailed astronomical observations. After Maxwell's equations became widely known, the Polish-American physicist Albert Michelson made a very precise measurement of the speed of light that was in extremely close agreement with Maxwell's predicted value. This was too much for Maxwell to accept as coincidence, and led him to the realization that light was an electromagnetic wave and thus part of the electromagnetic spectrum.

Comprehension Checkpoint

All electromagnetic waves travel at approximately

## The electromagnetic spectrum

As scientists and engineers began to explore the implications of Maxwell's theory, they performed experiments that verified the existence of the different regions, or groups of wavelengths, of the electromagnetic spectrum. As practical uses for these regions of the spectrum developed, they acquired now-familiar names, like "radio waves," and "X-rays." The longest wavelength waves predicted by Maxwell's theory are longer than 1 meter, and this band of the electromagnetic spectrum is known as radio waves. The shortest wavelength electromagnetic waves are called gamma rays, and have wavelengths shorter than 10 picometers (1 trillion times shorter than radio waves).

Maxwell's elegant equations not only unified the concepts of electricity and magnetism, they also put the familiar and much-studied phenomenon of light into a context that allowed scientists to understand its origin and behaviors. Maxwell appeared to have established conclusively that light behaves like a wave, but interestingly enough he also planted the seed of an idea that would lead to an entirely different view of light. It would be another thirty years before a young Austrian physicist named Albert Einstein would cultivate that seed, and in doing so spark the growth of a revolution in our understanding of how the universe is put together.

### Summary

The study of electricity and magnetism were artfully united in John Clerk Maxwell’s theory of electromagnetism. This module explores the experimental connection between electricity and magnetism, beginning with the work of Oersted, Ampere, and Faraday. The module gives an overview of the electromagnetic nature of light and its properties, as predicted by Maxwell’s mathematical model.

### Key Concepts

• In the mid-1800s, scientists including Andre Ampere and Michael Faraday noted a connection between electricity and magnetism and carried out a series of experiments that showed how they interact.

• James Clerk Maxwell built on the work of Faraday and developed a single set of equations defining both electricity and magnetism, unifying the concepts into one theory of electromagnetism.

• We now know that the electromagnetic spectrum is made up of a series of waves of varying wavelength and visible light is just one small portion of this spectrum.

• ##### NGSS
• HS-C4.3, HS-PS4.B1

Nathaniel Page Stites, M.A./M.S. “Light and Electromagnetism” Visionlearning Vol. PHY-1 (4), 2007.

Top