## Experiment IV-12

### waves of electric and magnetic fields

The connection between light and other phenonema was assumed by the followers of German Naturphilosophie.  There was considerable evidence to support this assumption:  It had always been recognized that the chemical reaction of a fire emits light.  Shortly after Volta created the electric battery in 1800 it was found that a wire heated by electricity also can glow.  Black objects absorb all visible light and colored materials absorb selected frequencies of light waves.  Substances such as Iceland Spar split polarized light waves.  And Faraday had shown in 1845 that the plane of polarization of light can be rotated by a magnetic field when light travels through a heavy glass.  But the precise connection was discovered by James Clerk Maxwell, (1831-1879, at left) of Scotland.

Michael Faraday (1791 - 1867) had envisioned lines of electric force originating of positive electric charges and terminating on negative charges.  These lines originated as a visualization aid with no real existence but Faraday felt that the space in which forces existed was itself modified so that the lines of force represent an actual field in that space.  A uniform field of electric force (such as shown at right) is created by two parallel conducting (metal) plates charged oppositely.  A positive electric charge placed in an electric field would experience a force in the direction of the lines of force.  Negative charges would experience a force in the opposite direction.  In other situations these lines need not be straight, but must be continuous following the path of least resistance.  For example they prefer to pass through a metal conductor in preference to through air.  The lines of force will follow the shape of such a conductor.

Electric charges are free to move through a conducting wire when driven by an electric field.  As discovered by Hans Christian Oersted in 1820, moving electric charges generate magnetic effects.  Faraday repeated Oersted's experiment and envisioned a magnetic field circular about the wire (as shown to left).  Note that if you wrap your right hand around the wire with your thumb facing in the direction of the current flow (from + to -), the magnetic field points the direction your fingers curl around the wire.  This right hand rule suggests that the north seeking pole of a magnetic compass will point in the direction of your fingers.  The magnetic field would be stronger near the wire and weaker further away.

If a wire conducting electric current is formed in the shape of a circular loop, a stronger magnetic field flux is produced inside the loop.  Additional loops forming a coil of wire increase the flux proportionally.

Physicists had long been used to understanding phenomena well enough to describe forces with equations.  While Faraday's electric and magnetic fields provided useful explanations for those phenonema, Faraday's lack of mathematical training prevented him from developing equations to describe the fields he described.  In 1855 after completing undergraduate studies at Cambridge University, James Clerk Maxwell became good friends with Faraday and undertook a decade long task of compiling equations that described Faraday's lines of electric and magnet forces

Some things were already known.  If a charge moves across to a magnetic field, the charge experiences a force (as does the field by Newton's third law) F = qv x B where the velocity and magnetic field strength B are vectors, and the force is the cross product at perpendicular to the plane generated by v and B.

Some of the equations for electricity and magnetism had been developed by Carl Friedrich Gauss (1777 - 1855), a professor of mathematics at the university of Göttingen, Germany.  Gauss rarely traveled away from home, but in 1828 he attended a conference in Berlin staying as house guest of Alexander von Humboldt.  Humboldt showed Gauss his collection of magnetic instruments, encouraging an interest in magnetism.  Gauss together with his assistant Wilhelm Weber (1804 - 1891), made numerous contributions to the field.  As Faraday defined, electric lines of force originate on charges.  Gauss suggested that this implies that the electric charge inside a closed volume (in this case the box at left) must be proportional to the net number of electric lines of force of leaving that volume. In mathematical terms, the strength of the electric field, E, through each small surface area, ds, summed over the entire two dimensional area depends on the charge, q.

Magnetic lines of force have no ends.  So Gauss found the strength of the magnetic field, B, through each small surface area, ds, summed over the entire two dimensional area (here, the box on the right) is zero because every entering magnetic line of force must also leave the volume.

Faraday had found that the changing number of magnetic lines of force passing though a imaginary loop (as shown below left) creates an electric field in the loop (and possibly a current if the loop is a conductor).  Maxwell expressed this mathematically by stating the CHANGE in the amount of magnetic flux with time (dB/dt) equals the Electric field in each section of loop (E•dl) summed around the entire one dimension loop.

A similar principle from Ampere states that the CHANGE in the amount of Electric flux crossing a bound area with time (dE/dt) equals the encircling Magnetic field (in each imaginary section of loop) (B•dl) summed around the entire length of loop (as shown below, right).

Maxwell realized that an electric field changing with time generates a magnetic field.  Originally he was considering the situation where charges in insulators are not free to flow but only vibrate from side to side momentarily creating what Maxwell called a displacement current.  But Maxwell realized the principle would still hold even in a vacuum region where no charges existed but an electric field might have been created by a changing magnetic field.  Combining the two ideas suggested that
an accelerated electric charge (e.g., by vibration or circular motion)
would be accompanied by a surrounding, changing magnetic field...
which would in turn create a changing electric field...
would be accompanied by a surrounding, changing magnetic field...
which would in turn create a changing electric field...
et cetera,
The original accelerated charge would create an unending sequence of time varying electric and magnetic fields which would produce an expanding wave-like phenonema.

A mechanical wave's speed depends on the stiffness and density of the medium through which it travels:
speed = √ stiffness / density.

Using the Faraday's lines of force model, Maxwell (found in Gauss's equations above) the electric constant,ε, equivalent to field stiffness and the magnetic constant, μ, equivalent to the density of the magnetic field.  Their ratio had the units of a speed and the value of 3.11 x 108m/sec.  Maxwell was immediately struck by the close similarity to the speed of light measured in 1849 by Armand Fizeau of 3.15 x 108m/sec.  Maxwell wrote This velocity is so nearly that of light, that it seems we have strong reason to conclude that light itself (including radiant heat, and other radiations, if any) is an electromagnetic disturbance in the form of waves propagated though the electromagnetic field according to electromagnetic laws.

Maxwell's effort to find mathematical equations for Faraday's fields provided a unified model, which accounted for all the then known phenomena of magnetism and electricity, much as Newton had two centuries earlier done for gravity and heavenly and earthly motions.  While Maxwell was convinced that light is an electromagnetic wave, other physicists were skeptical about the details of Maxwell's unified theory.  Maxwell improved on the agreement between the two speeds by experimentally comparing the attractions of two electric currents flowing in coils of wire (magnetic interaction), and the attraction or repulsion between two metal plates which have each received a charge of electricity (electric interaction).  Maxwell's electromagnetic theory was published in a semi-popular form in the Philosophical Magazine in 1861 and 1862.  Before confirmation and universal acceptance of his model, Maxwell died at age 48 apparently of an abominal cancer.

While visible light has a narrow range of frequencies between 4 x 1014 cycles/sec and 7 x 1014 cycles/sec, Maxwell had predicted a much wider range of electromagnetic waves could be produced.  Frederick William Herschel (1738-1822) had already discovered infrared light in 1800 and Johann Wilhelm Ritter (1776-1810) discovered ultraviolet light the following year.  But those had only slightly higher and lower frequencies than visible light.

In 1886, seven years after Maxwell's death, Heinrich Hertz demonstrated that Maxwell was indeed correct.  An spark caused by an oscillating current in one loop of wire would transmit a wave across some distance and drive a current around a nearby loop of wire.  In 1888 Hertz measured the time delay between the broadcast of the wave and its reception and found the speed of travel equal that of light.  Hertz went on the demonstrate that the radiation from his induced spark had all the usual properties of light.  In honor of his efforts he System International unit for measuring frequency, cycles per second, has been renamed the Hertz.

A 21 year old Italian, Guglielmo Marconi, read about Hertz's experiments.  In 1895 Marconi found that by increasing the power of the transmitter and stretching a wire high in the air for an antenna, and improving on the method of detection, the distance of transmission could be greatly increased.  By 1900 he had communicated with a detector 200 miles away.  In 1901 he detected in Ireland electromagmetic waves sent from Newfoundland showing the potential for long distance communication and revealing a layer of ions in the upper atmosphere of the earth which reflects radio waves.  Nowdays such electromagnetic waves shorter than 107 Hertz are called radio waves.

In 1906 F. A. Fressenden used a continuous oscillating current to produce a carrier radio wave allowing him to broadcast music carried by variations in the carrier wave amplitude (called AM radio) from Brant Rock, Massachusetts, and heard aboard U.S. naval ships nearby in the harbour.  Information such as music can also be carried by slight variations in the frequency of the carrier waves (called FM).  Television typically uses amplitude variations of the carrier to carry picture information and frequency modulation to carry the sound.  Cellular telephones and wireless computer networks use digital codes carried by electromagnetic carrier waves.

Rontgen discovered much higher frequency X-rays in 1896 (frequencies of 1017  to 1021 Hertz). Gamma rays with frequencies above 1020 Hertz were first detected the year following but not identified for another decade by Villard.

### Experiment

Cellular telephones, cordless telephones, wireless mice and many other remote devices use radio waves to transmit information.  These can be used to investigate various properties of electromagnetic waves.  You will need to obtain at least one of these devices for the following investigation.  The goal of this investigation is to demonstrate as many properties of electromagnetic radiation as possible.

### Procedure

The following procedure must be vague and general because the actual device you used for the investigation will be different from what others use.  DON'T use a high intensity device such as a microwave oven!  There are wide differences in the wavelengths and intensities of the electromagnetic waves used by different devices.  However the common properties of the electromagnetic waves can often be detected despite the differences.  Electromagnetic waves are used by transmitting them between a transmitting antenna and a detecting antenna.  Early in your investigation you will need to identify the general direction of the second device (transmitter or detector).

1. Electromagnetic waves are transmitted through many materials but absorbed by others.  Try placing various materials such as a sheet of paper, a thick book of paper, a sheet of moderately thick metal, plastic, and other available materials between the transmitter and detector.  If you can find a material that blocks the transmission of information, move it around to determine the general direction to the second device.

2. With the transmission (at least partially) blocked, investigate whether a second piece of the blocking material can reflect the waves past the blockage.  Investigate if, like we found with visible light, the angle of incidence waves equals the angle of reflected waves.

3. If for example you find that metal such as a cookie tray blocks the electromagnetic waves, try blocking or reflecting the waves with cooking trays that have parallel wires or slots.  Does the effect depend whether the wires or openings are turned vertical or horizontal?

4. Try turning the device vertically and horizontally.  Light and electromagnetic waves are transverse waves so they can be polarized.

5. Most modern digital devices have been engineered to not depend on the intensity of the waves carrying the signal.  So it might be difficult to detect properties that depend on signal intensity.  But it might be just possible under some circumstances to detect interference.  For example if a device is receiving a wave directly from the source and a second reflected wave from some material on the opposite side from the wave source a series of nodes and antinodes might be detectable.  Gradually change the distance between the device or the reflector searching for dead locations or nodes.  These appear one half wavelength apart so can be used to measure the size of the electromagnetic waves.

Record your observations recorded in your journal.  If you need course credit, use the information in your journal to construct a formal report.

### References

created 2/28/2001
latest revision 11/22/2004
by D Trapp