Measurement Of Magnetic Fields

Type of physical science: Classical physics

Field of study: Electromagnetism

Magnetic fields result from the flow of a current which aligns particles that are affected by the current. These fields can be measured by instruments that can be classified as absolute or relative. Absolute magnetometers do not need to be referenced to some other instrument or reading; relative magnetometers record values that are related to a fixed reading.

Overview

Magnets and their related fields are a part of daily life. Magnets decorate refrigerators at home as they hold up messages or recipes. Magnets are also present in doorbells, telephones, and audio and video equipment. Automatic teller machines are able to read the magnetic images on a credit card so that the proper bank account can be linked to the credit card. The same holds true for the strange-looking numbers on checks. Weak magnetic fields are imprinted into these numbers so that the check-processing equipment can debit the proper account.

A body becomes magnetized when it is placed in a magnetic field that is produced by an electrical current or by a magnet (which has itself been magnetized by a current). Only substances whose internal atomic properties allow their electrons to be affected by a magnetic field can become magnetized. If it is assumed that some particles within an atom are in continuous motion, it is easier to see that when a substance is subjected to a magnetic field, some of the moving particles within the atoms of the substance can have their motion altered by the magnetic field.

The theory and mathematics of magnetic fields is rather complex. Physicists and mathematicians have realized that a complex problem often can be reduced to more simple models. The concept of the dipole thereby helps to visualize a magnetic field, making it easier to understand. Most bodies that can be magnetized can have their magnetic source modeled as a simple bar magnet that has two poles--a north pole and a south pole. The existence of these two poles implies that there is a continuous magnetic field within the body. If the bar magnet is broken in half, each new half then has a separate north and south pole. There is no way to isolate a single pole. Because the two poles are opposite to each other, each has a different charge. Lines of magnetic force are produced which extend from one pole to the other. This is seen clearly when iron filings are placed on a sheet of paper and a bar magnet is placed under the paper.

There is a field near each separate pole, which is attributable to the pole itself.

Magnetic fields can be described in terms of several measurable units. Because magnetic fields operate in space, these measurable units are actually vectors. The magnetic field vector B is defined as the lateral force F _B, which acts upon a particle having charge q and moving with some velocity v. (The bold letters refer to the fact that these variables are vectors, items that have both magnitude and direction associated with them.) It is more practical to speak of magnetic fields in terms of their magnetic field strength (H). B and H are related to each other by the constant of magnetic permeability μ(B = μH).

Several types of magnetism exist in nature. The degree to which these types of magnetism are found in a substance can be described in terms of the substance's magnetic susceptibility. The three major groups that are used to categorize all materials (elements, compounds, and the like) are diamagnetic, paramagnetic, and ferromagnetic. Diamagnetic materials have a "negative" magnetic susceptibility, which means that the substance is magnetized in the opposite direction of an applied field. Diamagnetism exists in all substances but is generally masked by one of the more dominant conditions of paramagnetism or ferromagnetism. Diamagnetism is a characteristic of atoms having completely filled electron shells, such as the rare gases (for example, neon and argon).

Paramagnetic substances have a "positive" magnetic susceptibility. On an atomic scale, paramagnetism is a characteristic of elements whose subshells are not filled completely with electrons. The most notable elements in this classification are those metals lying between calcium and nickel in the periodic table. Ferromagnetic materials are those in which the magnetic interaction between atoms and groups of atoms is strong enough to produce an alignment of dipoles in parallel. This alignment is strong enough to allow the substances to maintain a magnetic field of their own, once they have become magnetized and the source is removed. The best examples of ferromagnetic substances are iron, cobalt, and nickel. If these metals are heated above a temperature known as the Curie temperature, the induced field is lost and the substance reverts to being paramagnetic. The Curie temperature for iron is 1,043 Kelvins, which means that iron located deep within the earth cannot maintain a magnetic field. The same holds true for both iron and nickel located in the earth's inner core.

Applications

The earth's magnetic field is described in terms of its total force (F), horizontal component (H), and vertical component (Z). Different instruments measure different values of the field. Perhaps the most common measurement of magnetics involves that of the earth's field in order to determine a direction. This measurement is done by using a magnetic compass, an instrument that uses the directional force of the earth's magnetic field to record the horizontal component of the magnetic field at a particular location on the earth's surface. Such an instrument contains a magnetized needle that is situated on a fixed point so the needle is free to rotate. Thus, the needle is a simple dipolar magnet. The principle that allows the compass to work is that similar magnetic poles repel each other or, rather, that opposite poles attract each other. By standardized convention, the needle points to the northern direction so that the end of the needle (which often has a dot or some other distinguishing mark on it) is the north-seeking pole of the needle. Thus, the north pole is so named because it is the north-seeking pole. Magnetic north does not correspond to geographic north. The magnetic north pole is currently located near 76.1 degrees north and 100 degrees west. This position changes through time. North is the reference pole for most scientists, except surveyors and astronomers who use the south pole.

Another major purpose for measuring magnetic fields is to determine the magnitude of the earth's magnetic field at different locations on the earth. This measurement is important from a positional or navigational standpoint--be it engineers locating paths for highways, scientists working in the field, or the military determining directions for firing artillery or rockets. In determining the magnitude and direction of the earth's magnetic field, three primary parts must be considered which contribute to the field at any given location. The main field, which is of internal origin, is a slowly changing field that varies with time and position. This field is caused by the internal source that is related to the differential movement of the earth's mantle and outer core. An external field, although small in magnitude, can vary quite radically. This field occurs in the form of intermittent magnetic storms, which can disrupt anything associated with the magnetic field. During magnetic storms, communications are disrupted as well as any field work or research requiring a stable magnetic field. Finally, small, local variations caused by localized magnetic bodies can produce significant anomalies, which must be accounted for when taking magnetic readings.

Measurements of magnetic fields can be made in the laboratory or outdoors in the actual field setting, which produces large-scale naturally occurring values. Laboratory measurements are necessary to determine the susceptibility of magnetic materials. Ferromagnetic materials have the greatest magnetic susceptibility and are, therefore, the most likely to become magnetized and to maintain the field once the source is removed.

Any magnetic measuring instrument must be able to measure very small differences in magnetic values. For example, a good magnetometer is capable of detecting changes on the order of 0.01 to 0.5 nanotesla in a total value of about 10^-4 teslas. As is true with any developing technology, there has been a steady refinement of the instruments used to measure the force components F (total field), Z (vertical component of F), and H (horizontal component of F). When considered in the context of the earth's field, magnetometers can be grouped into two categories: absolute and relative instruments.

Absolute magnetometers can make measurements without having to be calibrated to some standard reference value. Relative instruments are first referenced, or standardized, to some known magnetic field before readings can be taken. In this case, the relative readings must then be related back to the established, standard value before an interpretation can be made.

Since the early 1800's, when Carl Friedrich Gauss constructed the first crude magnetometer, there have been many different types of instruments. Included among the absolute magnetometers are the nuclear precession and sine magnetometers; relative instruments include the Schmidt field balance, flux gate, and rubidium (or cesium) vapor magnetometers.

Nuclear precession magnetometers measure the total magnetic field (F). These instruments are the most commonly used throughout the world, primarily because of their accuracy and the small amount of time needed to take readings. Accuracies in the range of about 0.5 nanotesla can be obtained in less than five seconds. The principle under which this instrument operates is based on the measurement of the frequency of freely spinning hydrogen nuclei (protons) that have been polarized in a direction roughly perpendicular to the direction of the earth's field. These spinning (precessing) protons continue to spin when the polarizing field is suddenly removed. The force required for these protons to continue spinning is what is measured, thus yielding the magnitude of the field at the location of measurement. The internal configuration of the nuclear precession magnetometer includes a small amount of water (source of the protons) or some other fluid that contains a high concentration of hydrogen, such as benzene or methanol. A small solenoid is wrapped around the container holding the fluid. As a direct current is passed through the solenoid, the resulting polarizing field causes the protons to spin. The amount of precession is detected by another coil, which sends the signal to an amplifier that then records the value. The nuclear precession magnetometer has several advantages. It is very sensitive, measures the total field, and does not need to be balanced or oriented in any specific direction. Because of its versatility, it is often used in airplanes and ships to make magnetic measurements. Primary disadvantages include the instrument's inability to measure components of the field without some modification of the instrument and its need to "rest" between readings, as the polarizing field must build up to a maximum before a subsequent reading can be made. The instrument can be adapted for both aeromagnetic and shipboard surveys.

The sine magnetometer consists of a hollow marble cylinder around which a Helmholtz coil system has been wound. Precise measurements of the coil dimensions are necessary for accurate results. A small magnet, suspended in the marble coil, is deflected when a known current is passed through the Helmholtz system. The position of the magnet prior to its deflection depends on the intensity of both the earth's field and the coil, along with the distance the coil must be rotated to maintain alignment of the magnet and coil.

Relative magnetometers are those that must be calibrated to known values. One of the most common relative instruments is the flux gate magnetometer, which was developed during World War II to detect submarines from aircraft. This magnetometer uses a saturated core sensor, which is oriented in a vertical position to measure the vertical component of the earth's magnetic field. These instruments lack the sensitivity of precession instruments and also have the obvious shortcoming of measuring only the vertical field. In order to maintain accuracy, the flux gate magnetometer must be aligned in a vertical sense. The core of the flux gate consists of magnetic material with a relatively high permeability in low magnetic fields. This core is commonly structured so that there is a pair of cores, each wound with primary and secondary coils in such a fashion that they are in opposite directions to each other. These cores are then subjected to a low-frequency current, which is produced by activating a constant current source. The resulting current magnetizes the cores with opposing polarities. The secondary coils are wired to an amplifier, whose output is proportional to the difference in the input signals. Through a series of electrical connections, the flux gate is configured so that the outputs of the secondary coils negate each other. Thus, whenever a component of an external field is measured (in this case, the vertical component), there is a temporary induction of this external field into the secondary cores.

This induction lasts for a brief time only, but long enough to produce a voltage that can be recorded as the strength of the field at that point. There are several problems in the overall design and theory of the flux gate magnetometer that are related to the electrical configuration of the instrument. Nevertheless, these problems are minor and are offset easily by its distinct advantages, which include light weight, portability, direct readout, and course-leveling requirements that produce rapid readings (usually less than thirty seconds). In addition, depending on how the cores are aligned within the instrument, it can be used for either vertical (most common) or horizontal field measurements.

Another type of relative instrument, which was used extensively in the early days of petroleum exploration, is the Schmidt vertical magnetic field balance. The design is very basic in that a magnetic bar is centered almost on a knife-edge pivot. The center of balance of the bar magnet is offset slightly to counter gravitational attraction of the bar's mass. The torque produced by the magnetic field is such that it counters the gravitational attraction. A mirror system allows one to measure the angle at which equilibrium is attained; this angle is proportional to the strength of the earth's magnetic field at the reading location. The optical and mechanical systems in the Schmidt field balance must be exceedingly precise in order to obtain accurate readings.

This instrument is much more delicate than the other relative instruments.

A third type of relative instrument, which measures total field values, is the rubidium (or cesium) vapor magnetometer, which was introduced in the 1960's. The principle involved in the operation of this magnetometer is that of measuring the energy it takes to move electrons within different orbits of an atom. The actual procedure relies on a technique called "optical pumping," which involves moving the electrons to higher energy levels within an atom. (For the details of this procedure, the reader is referred to an article entitled "Optical Pumping" by Arnold Bloom, 1960.) The orbits that an electron can occupy within an atom are limited. Movement of an electron can take place from a higher energy level to a lower one or from a lower energy level to a higher one. The energy change is in the form of electromagnetic radiation. If an external source--such as the earth's magnetic field--is applied to an atom, there can be a shift of an electron to a higher orbit level.

The valence electron of an alkali metal, such as rubidium or cesium, exists in two states: a normal level (N) and an excited level (E). When subjected to an external force, each state divides itself into a pair of levels (N₁ and N₂; E₁ and E₂). The differences (N₁ - E₁ and N₂ - E₂) are proportional to the external force.

Therefore, if the total magnetic field is serving as the external energy source, it is possible to determine the magnitude of the earth's total magnetic field.

Context

Magnetic materials have been recognized since the Stone Age, but it was not until the early nineteenth century that scientists were able to recognize and describe the physical situations that produced magnetic substances and their related fields. The work of Gauss and others established the mathematical and physical basis of the study of magnetics. Much of the research and application of magnetic field studies resulted from World Wars I and II. The major combatants in each of these wars realized it was necessary to devise ways to detect the enemies' aircraft and submarines; therefore, much money and effort were directed to refining the means to measure and detect metallic bodies.

The measurement of magnetic fields is carried out in order to determine the strength and direction of the components of the field. Scientists can determine the magnitude and direction of magnetic fields either in the laboratory or in the field. In either case, the measured values can be related to some type of source, whether it is natural, induced, or otherwise.

Magnetic fields associated with small bodies can be measured and then the values can be used to estimate theoretically the magnetic field associated with a larger body of the same material. In nature and on a large scale, magnetic fields such as those associated with Earth or the planets can be measured using similar techniques developed for smaller bodies.

Numerous experiments can be set up to measure magnetic fields in the laboratory.

Specific experiments, such as those detailed by Arthur Hovey (1989) and B. J. Pernich (1989) in the AMERICAN JOURNAL OF PHYSICS, lend a sense of order to an area of physics that many find confusing.

Principal terms

DIPOLE: a pair of equal magnetic poles of opposite sign that are separated by a small distance

MAGNETIC FIELD: a condition produced when two or more moving charges produce kinetic energy and momentum as the result of an electric current or magnet

MAGNETIC FIELD INTENSITY: a vector quantity that measures the strength of the magnetic field; this value is often expressed in terms of the density of lines of force representing the field

MAGNETOMETER: an instrument used to measure the strength and direction of the earth's magnetic field at some specific location

PERMEABILITY: a measure of the change in the force of attraction or repulsion between two magnetic poles; this depends on the properties of the specific material being affected by the magnetic field

SUSCEPTIBILITY: the ability of a substance to become magnetized

TESLA: the unit of measurement of magnetic fields; one tesla equals one newton (coulomb times meter per second)

Bibliography

Bloom, Arnold L. "Optical Pumping." SCIENTIFIC AMERICAN 203 (October, 1960): 72-80. One of the first articles written for the nontechnical reader that clearly explains the procedure to alter the energy level of atoms to use them to measure magnetic fields. Geared for high school students and above. Well illustrated.

Halliday, David, and Robert Resnick. FUNDAMENTALS OF PHYSICS. 3d ed. New York: John Wiley & Sons, 1988. This widely used college-level text provides an introductory mathematical description of magnetic fields. Gives some insight into the measurement of magnetic fields.

Hovey, Arthur. "On the Magnetic Field Generated by a Short Segment of Current." AMERICAN JOURNAL OF PHYSICS 57 (July, 1989): 613-616. The author provides an experiment, which has a calculus-based solution, for the more advanced high school student. This experiment shows the effects of the position of the recording instrument with respect to the source, and how the resulting field changes with position and distance.

MCGRAW-HILL ENCYCLOPEDIA OF SCIENCE AND TECHNOLOGY. 6th ed. 20 vols. New York: McGraw-Hill, 1987. This set contains detailed entries on specific topics and terms associated with magnetic fields. Many of the articles contain an abbreviated list of references. Suitable for high school students and the general reader.

Parker, Sybil P., ed. MCGRAW-HILL CONCISE ENCYCLOPEDIA OF SCIENCE AND TECHNOLOGY. 2d ed. New York: McGraw-Hill, 1989. A single-volume text that has abbreviated entries of the expanded set cited above. Useful for the general reader interested in brief explanations where detail is not necessary.

Pernich, B. J. "Simultaneous Measurement of the Straight Wire and the Earth's B field." AMERICAN JOURNAL OF PHYSICS 57 (January, 1989): 90-91. Outlines a simple experiment that can be performed in a high school physics laboratory. The associated mathematics are provided in detail for further explanation of the phenomenon.

Telford, W. M., L. P. Geldart, R. E. Sheriff, and D. A. Keys. APPLIED GEOPHYSICS. 2d ed. Cambridge, England: Cambridge University Press, 1990. A college-level textbook that gives an excellent summary of the relationship of the earth's magnetic field to its geologic setting and sources.

Forces on Charges and Currents

Magnetic Properties of Solids