Introduction to Magnetism and Induced Currents

Intro to Magnetism: Sources of Magnetic Fields Magnetic Fields and Forces
Induced Currents: Faraday's Law
Induction and Magnetic Recording
Summary

Despite the increasing prevalence of CD-ROMs and the use of electronic storage in RAM, most data is still stored magnetically.  This reading assignment reviews the basic concepts of magnetism, then introduces the three different effects which have been utilized to read magnetic data.

Sources of Magnetic Fields


Discussion Question:  What produces magnetic fields?  Is there any difference between the fields of permanent magnets and the fields of electromagnets?  Are the sources of the fields the same in these two cases, or are they different?

Our thinking about magnetic sources has changed considerably over the centuries.  The only form of magnetism known until the 19th century was ferromagnetism.  Certain materials, when "magnetized", would attract certain other materials.  The only materials attracted by a magnet were those that could become magnetized themselves.  Since only certain materials exhibited magnetic properties, scientists concluded that magnetism was an inherent property of materials.

Then, in the 19th century, scientists studying the relatively new field of electrical currents discovered that moving charges produce magnetic effects.  A current traveling through a loop of wire creates a magnetic field along the axis of the loop.  The direction of the field inside the loop can be found by curling the fingers of the right hand in the direction of the current through the loop; the thumb then points in the direction of the magnetic field.  With this discovery, magnetism appeared to occur in two different manners:  ferromagnetism depending on the material, and electromagnetsim caused by currents.
 
 
Classical views of the (a) orbital motion 
and (b) spin of an electron.
As atomic physics and chemistry began to explain the periodic table with the help of the Bohr model of the atom  in the early 1900s, magnetic properties were assigned to the electrons in atoms.  Electrons appeared to exhibit two types of motion in an atom:  orbital and spin.  Orbital motion referred to the motion of an electron around the nucleus of the atom.  Since a charged particle was moving, a magnetic field was created.  But electrons (and protons and other particles) also appeared to be spinning around their centers, creating yet another magnetic field.  The magnetic field due to the orbital motion and the magnetic field due to the spin could cancel or add, but expressions for the exact coupling between the two are too complicated to go into here.  Since electrons were moving and spinning within atoms, ferromagnetism could now be explained by the motion of charges within different materials.  If all of the electrons in an object line up with their spins in the same direction, the spins will add and create an observable field.

 
That last sentence is slightly unrealistic.  Solids contain incredably large numbers of electrons, and they will never all completely line up.  Instead, a solid generally consists of magneticdomains.  In a domain, the majority of electrons which can (unpaired valance electrons) will have spins aligned.  Adjacent domains will generally not be oriented in identical directions.  In magnetized materials, some domains will cancel, but the average domain orientation will be in one direction, producing a net magnetic field.  In unmagnetized materials, the domains are randomly oriented and cancel, so no observable field is created.  The figure to the right illustrates these concepts.

The concept of magnetism being entirely due to the motion of charges has been modified significantly in the 20th century, thanks to quantum mechanics.  The Bohr model of the atom must be modified to include uncertainty.  We can never determine exactly the trajectory of an electron or say for certain where it will be found.  The uncertainty principle requires that we instead say only where the electron is most likely to be found.  Until we measure the position of the electron, its wave function is spread out over all space, with a higher probability of finding the electron in the classical orbit described by Bohr.

 


(a)
Sample electron spins 
in a solid.  Not all are
aligned, but . . .

(b)
. . . when canceling spins
are accounted for, a net
magnetic field remains.

(c)
This residual field in a 
region is the net magnet-
ization of the region, or 
domain.

(d)
Solids contain several
such domains, which 
are generally not 
aligned completely, but

(e)
The fields of the individual 
domains in a magnetized 
solid don't completely cancel
but leave a net field

(f)
In an unmagnetized solid
the fields of nearby
domains completely
cancel,  leaving no net field

Our concept of spin must also be adjusted to fit with the discoveries of the 20th century.  Electrons are thought to be "point particles," which means they have no spatial extent.  Which means they can't be physically spinning around their centers.  While the word "spin" has survived, it now refers to an intrinsic property of a particle rather than to any physical rotation through space.  Since electrons and other particles have intrinsic spin, they create magnetic fields automatically.  After considering quantum mechanics, we are once again left with two types of magnetism:  intrinsic magnetism due to the "spins" of electrons, and electromagnetism due to the motion of electrons.

Just as an aside, the reason that molecules such as He are not magnetized is the Pauli exclusion principle.  The two electrons in helium atoms occupy the same energy shell, filling it (the first shell contains only 2 states).  The exclusion principle states that no two electrons can have the same exact properties.  For them both to occupy the same energy shell, their spins must be oppositely directed and cancel.  Electrons in solids with partially-filled valence shells may, however, line up with the same spin as other electrons, thereby creating a non-zero net magnetic field.
 

Magnetic Fields and Forces



Discussion Question: Think about what you have learned during your lifetime about electricity and magnetism.  How are they alike?  How are they different?  Any charged object in an electric field experiences an electric force.  Will any charged object in a magnetic field experience a magnetic force?  Does an object have to be charged to experience a magnetic force?

Magnets can exert a force at a distance, just like electric charges.  So it is advantageous to describe the effects of magnets in terms of a magnetic field, B1, much in the same way that the effects of charges are described by the electric field.  We have already invoked this concept of a magnetic field in the previous section.  Magnetic fields permeate space and are strongest near a permanent magnet or electromagnet.  IThe SI unit for B is the tesla (1 T = 1 Vs/m2).  The tesla is a fairly large unit of magnetic field, so we often list magnetic field strengths in terms of Gauss (1 G = 10-4 T).  The magnetic field of the earth is about one-half gauss in strength.
Like an electric field, a magnetic field may be represented with field lines.  These lines (and the magnetic field) point from the north pole of a magnet to the south pole of a magnet, as shown in the figure to the left..  Unlike electric field lines, magnetic field lines are always closed - they never have a starting point or stopping point.  Whenever you have a north pole, you must have a south pole as well.  Another way to say this is that magnetic monopoles (single poles) do not exist.  Electric monopoles, on the other hand, exist in abundance.  Examples are an electron, a proton, or any other charged particle.
Even the magnetic field produced by a current-carrying wire must form complete loops.  Above, you were told that a loop of current-carrying wire produces a magnetic field along the axis of the wire.  The right-hand rule gives the direction of the field inside the loop of wire.  The magnetic field turns back the other way outside of the loop.  As shown in the figure on the right, this magnetic field from a loop of current-carrying wire looks similar to the field from a permanent bar magnet.

Anyone who has used a compass knows that a magnet experiences a force in a magnetic field.  Just as for electric charges, opposite magnetic poles repel and like poles attract.  Thus the magnetic field pointing from north to south points in the direction of the force on a NORTH POLE of a magnet.  One interesting result of this is that the Earth's geographic north pole is its magnetic south pole.  A compass needle's magnetic north pole will point toward the geographic north pole of the Earth.  Since the north pole of a magnet is attracted to the south pole of another magnet, this means that the geographical north pole of the Earth is really a south magnetic pole.

Permanent magnets are not the only objects which experience the magnetic force.  Electric charges can experience a magnetic force if two conditions are met:

  1. The charge must be moving through a magnetic field
  2. The velocity of the charge cannot be parallel (or antiparallel) to the direction of the magnetic field
The magnitude of the force is proportional to the charge q, the magnetic field B, the speed of the charge v, and the sine of the angle q between the velocity and the magnetic field:

FB = qvB sin q

The direction of the force is perpendicular to both the velocity and the magnetic field.  The force is more accurately expressed in terms of a cross-product:

FB = qv x B

The magnitude of a cross-product depends on sin q, giving the previous expression.  For our purposes, the first expression is sufficient, provided you remember that the force is perpendicular to both the velocity and the magnetic field.

A current-carrying wire also experiences a force in a magnetic field, since current is nothing more than moving charges.  As for single charges, the current must be moving in a direction other than the direction of the field.  The magnitude of the magnetic force on a current-carrying wire is found from

FB = iLB sin q

where i is the current and L is the length of wire in the uniform magnetic field of strength B.
 
 
1 To be exact, the symbol B represents magnetic flux density, also called magnetic induction, not magnetic field.  The true magnetic field is denoted by HH and B differ only by a material-dependent constant.  For most purposes, the difference is inconsequential, so we will refer to B as the magnetic field.  If you take further courses in magnetism, you will learn the distinction.

 

Induced Currents, Induced EMF, and Faraday's Law



Discussion Question: Can you create a current through a wire without connecting the wire directly to a voltage source like a battery?  Do all of your appliances have direct connections?  What about your car engine?

If a coil of wire is placed in a changing magnetic field, a current will be induced in the wire.  This current flows because something is producing an electric field that forces the charges around the wire.  (It cannot be the magnetic force since the charges are not initially moving).  This "something" is called an electromotive force, or emf, even though it is not a force.  Instead, emf is like the voltage provided by a battery.  A changing magnetic field through a coil of wire therefore must induce an emf in the coil which in turn causes current to flow.

The law describing induced emf is named after the British scientist Michael Faraday, but Faraday's Law should really be called Henry's Law.  Joseph Henry, an American from the Albany area, discovered that changing magnetic fields induced current before Faraday did.  Unfortunately, he lived in the age before instantaneous electronic communication between Europe and America.  Faraday got published and got famous before Henry could report his findings.  Interestingly enough, Henry had to explain the results to Faraday when the two met a few years later.

Briefly stated, Faraday's law says that a changing magnetic field produces an electric field.  If charges are free to move, the electric field will cause an emf and a current.  For example, if a loop of wire is placed in a magnetic field so that the field passes through the loop, a change in the magnetic field will induce a current in the loop of wire.  A current is also induced if the area of the loop changes, or if the area enclosing magnetic field changes.  So it is the change in magnetic flux, defined as

that determines the induced current.  A is the area vector; its magnitude is the area of the loop, and its direction is perpendicular to the area of the loop, and q  is the angle between A and the magnetic field B.  The last equality (removing the integral) is valid only if the field is uniform over the entire loop.

Faraday's Law says that the emf induced (and therefore the current induced) in the loop is proportional to the rate of change in magnetic flux:

e is the emf, which is the work done moving charges around the loop, divided by the charge.  It is similar in concept to voltage, except that no charge separation is necessary.  The magnetic flux FB equals the magnetic field B times the area A of the loop with magnetic field through it if (a) the magnetic field is perpendicular to the plane of the loop, and (b) the magnetic field is uniform throughout the loop.  For our purposes, we will assume these two conditions are met; in practical applications, however, magnetic field will vary through a loop, and the field will not always be perpendicular to the loop.

Since all applications of Faraday's Law to magnetic storage involve a coil of wire of fixed area, we will also assume that (c) the area does not change in time.  We then have a simpler expression for the current induced in the coil:

The induced current depends on both the area of the coil and the change in magnetic field.  In a coil of wires, each loop contributes an area A to the right-hand side of the equation, so the induced emf will be proportional to the number of loops in a coil.  But doubling the number of loops doubles the length of wire used and so doubles the resistance, so the induced current will not increase when loops are added.
 
 

Induction and Magnetic Recording

A traditional recording head for magnetic data consists of a coil of wires attached to some current-sensitive device.  A ferromagnetic material passes under the coil.  Such an arrangement can both write magnetic data to the ferromagnetic material and read magnetic data off of the material.

To write magnetic data, current is sent through the coil in proportion to the desired signal.  This current produces a magnetic field proportional to the current.  The magnetic field aligns the spins in the ferromagnetic material.  As the material moves away from the coil, the magnetic field decreases, and the spins remain aligned until they enter another magnetic field (when they are erased).

Unlike electric storage, magnetic storage can be either analog or digital.  The amount of spin alignment depends on the strength of magnetic field, so analog data can be recorded with a continually varying current producing a continually varying magnetic field.  Digital data can be recorded by alternating the direction of the current.  To minimize data loss or errors, binary data is not determined solely by the direction of magnitization in a domain.  Instead, it is represented by the change in magnetic orientation between two domains.  If one bit of magnetic field has the same direction as the one before it, that represents a 0 (no change).  If one bit of magnetic field has the opposite direction as the one before it, that represents a 1 (change).  So a 1 is written by changing the direction of current between the two domains comprising a bit, and a 0 is written by keeping the direction the same.  Each bit starts with a change of orientation.  This convention for recording data identifies errors, since one would never have three domains of the same orientation in a row.  In addition, the orientation should change with every other domain.  If the computer thinks a bit is complete but the orientation does not change, it knows that some error has occurred.  Some examples of domains, bits, and strings are shown below.

To read magnetic data, the ferromagnetic material is moved past the coil of wire.  The changing magnetic field caused by the material's motion induces a current in the coil of wire proportional to the change in field.  If a 0 is represented, the magnetic field does not change between the two domains of a bit, so no current is induced as the magnetic material passes the coil.  For a 1, the magnetic field changes from one direction to the other; this change induces a current in the coil.

Inductive reading of magnetic data is subject to many limitations.  Since the change in magnetic field will be greater if the ferromagnetic material is moved faster, the induced current is dependent on the speed of the material.  Thus the sensitivity of inductive read heads is limited by the precision of the material speed.  The other limiting factor on inductive heads is the strength of the magnetic field.  As efforts to increase storage density continue, the size of a data element shrinks.  Since fewer electrons are now contained in the region of one bit, the associated magnetic field is smaller.  This smaller magnetic field produces less change and thus less induced current, requiring more loops to produce a measurable current.  As mentioned above, more loops means more resistance which means more heat.  Because of these limitations, new magnetic storage devices use the phenomenon of magnetoresistance to read magnetic data.
 

Summary


Facts About the Force
(From Driving Force:  The Natural Magic of Magnets, by James D. Livingston, (Havard University Press: Cambridge), 1996)

These 10 facts about the force from Driving Force by Livingston summarize most of the information contained in this and the next reading.  Of particular interest to the workings of computers are steps 4, 6, and 8.  9 and 10 are also important concepts to remember.  This reading assignment has only touched on the applications of magnets in information systems and other commonly-used technologies.  If you are interested in learning more, the book by Livingston is an excellent place to start.
 
1. If free to rotate, permanent magnets point approximately north-south.
2. Like poles repel, unlike poles attract.
3. Permanent magnets attract some things (like iron and steel) but not others (like wood or glass).
4. Magnetic forces act at a distance, and they can act through nonmagnetic barriers (if not too thick).
5. Things attracted to a permanent magnet become temporary magnets themselves.
6. A coil of wire with an electric current flowing through it becomes a magnet.
7. Putting iron inside a current-carrying coil greatly increases the strength of the electromagnet.
8. Changing magnetic fields induce electric currents in copper and other conductors.
9. A charged particle experiences no magnetic force when moving parallel to a magnetic field, but when it is moving perpendicular to the field it experiences a force perpendicular to both the field and the direction of motion.
10. A current-carrying wire in a perpendicular magnetic field experiences a force in a direction perpendicular to both the wire and the field.

Suggested Additional Reading

All sources for Additional Reading are on reserve at the library or available for perusal in the instructor's office.  Students are encouraged to access these readings, as they provide photographs and illustrations not available for inclusion in these web-based readings.

Driving Force:  The Natural Magic of Magnets, by James D. Livingston, (Havard University Press: Cambridge), 1996.  An extremely good book about magnetism and their applications in our everyday activities.  It's cheap, too (about $12+shipping from Amazon, VarsityBooks, BigWords, or barnesandnoble.com).

Computing: The Technology of Information, by Tony Dodd.  (Oxford University Press: New York), 1995.  Pages 70-71 include short description of capacitors in DRAM.

How Computers Work, by Ron White.

The Cartoon Guide to Physics, by Larry Gonick and Art Huffman.  (Harper Perennial: New York), 1991.  This is a great user-friendly treatment of the basic concepts in phsyics, including magnetism and induction.

Any introductory physics text, such as Fundamentals of Physics by Halliday, Resnick and Walker.
 


Copyright © 2001-2002 Doris Jeanne Wagner.  All Rights Reserved.