Introto Magnetism:Sourcesof Magnetic FieldsMagneticFields and Forces
InducedCurrents:Faraday"sLawInductionand Magnetic Recording
Despite the increasing prevalence of CD-ROMsand the use of electronic storage in RAM, most data is still stored magnetically.This reading assignment reviews the basic concepts of magnetism, then introducesthe three different effects which have been utilized to read magnetic data.

Sourcesof Magnetic Fields

Discussion Question:
Classical views of the (a) orbital motionand (b) spin of an electron.As atomic physics and chemistry began to explain the periodic tablewith the help of the Bohr model of the atom in the early 1900s, magneticproperties were assigned to the electrons in atoms. Electrons appearedto exhibit two types of motion in an atom: orbital and spin.Orbital motion referred to the motion of an electron around the nucleusof the atom. Since a charged particle was moving, a magnetic fieldwas created. But electrons (and protons and other particles) alsoappeared to be spinning around their centers, creating yet another magneticfield. The magnetic field due to the orbital motion and the magneticfield due to the spin could cancel or add, but expressions for the exactcoupling between the two are too complicated to go into here. Sinceelectrons were moving and spinning within atoms, ferromagnetism could nowbe explained by the motion of charges within different materials.If all of the electrons in an object line up with their spins in the samedirection, 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 neverall 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 orientedin identical directions. In magnetized materials, some domains willcancel, but the average domain orientation will be in one direction, producinga net magnetic field. In unmagnetized materials, the domains arerandomly 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 chargeshas been modified significantly in the 20th century, thanks to quantummechanics. The Bohr model of the atom must be modified to includeuncertainty. We can never determine exactly the trajectory of anelectron or say for certain where it will be found. The uncertaintyprinciple requires that we instead say only where the electron is mostlikely to be found. Until we measure the position of the electron,its wave function is spread out over all space, with a higher probabilityof finding the electron in the classical orbit described by Bohr.(a)Sample electron spinsin a solid. Not all arealigned, but . . .(b). . . when canceling spinsare accounted for, a netmagnetic field remains.(c)This residual field in aregion is the net magnet-ization of the region, ordomain.
(d)Solids contain severalsuch domains, whichare generally notaligned completely, but(e)The fields of the individualdomains in a magnetizedsolid don"t completely cancelbut leave a net field(f)In an unmagnetized solidthe fields of nearbydomains completelycancel, leaving no net field
Our concept of spin must also be adjusted to fit with the discoveriesof the 20th century. Electrons are thought to be "point particles,"which means they have no spatial extent. Which means they can"t bephysically spinning around their centers. While the word "spin" hassurvived, it now refers to an intrinsic property of a particle rather thanto any physical rotation through space. Since electrons and otherparticles have intrinsic spin, they create magnetic fields automatically.After considering quantum mechanics, we are once again left with two typesof 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 magnetizedis the Pauli exclusion principle. The two electrons in helium atomsoccupy the same energy shell, filling it (the first shell contains only2 states). The exclusion principle states that no two electrons canhave the same exact properties. For them both to occupy the sameenergy 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-zeronet magnetic field.

MagneticFields and Forces

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 amagnetic field, B1, much in thesame way that the effects of charges are described by the electric field.We have already invoked this concept of a magnetic field in the previoussection. Magnetic fields permeate space and are strongest near apermanent magnet or electromagnet. IThe SI unit for B is thetesla(1 T = 1 Vs/m2). The tesla is a fairly large unit of magneticfield, 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-halfgauss in strength.
Like an electric field, a magnetic field may be represented with fieldlines. These lines (and the magnetic field)point from the northpole of a magnet to the south pole of a magnet, as shown in the figureto the left. Unlike electric field lines, magnetic field lines arealways 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 notexist. 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 formcomplete loops. Above, you were told that a loop of current-carryingwire produces a magnetic field along the axis of the wire. The right-handrule 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 ofcurrent-carrying wire looks similar to the field from a permanent bar magnet.
Anyone who has used a compass knows that a magnet experiences a forcein a magnetic field. Just as for electric charges, opposite magneticpoles repel and like poles attract. Thus the magnetic field pointingfrom north to south points in the direction of the force on a NORTH POLEof a magnet. One interesting result of this is that the Earth"s geographicnorth pole is its magnetic south pole. A compass needle"s magneticnorth 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 anothermagnet, this means that the geographical north pole of the Earth is reallya south magnetic pole.Permanent magnets are not the only objects which experience the magneticforce. Electric charges can experience a magnetic force if two conditionsare met:The charge must be moving through a magnetic fieldThe velocity of the charge cannot be parallel (or antiparallel) to thedirection of the magnetic fieldThe magnitude of the force is proportional to the charge q, themagnetic field B, the speed of the charge v, and the sineof the angle q between the velocity and themagnetic field:FB = qvB sin qThe direction of the force is perpendicular to both the velocity andthe magnetic field. The force is more accurately expressed in termsof a cross-product:FB = qv x BThe magnitude of a cross-product depends on sin q,giving the previous expression. For our purposes, the first expressionis sufficient, provided you remember that the force is perpendicular toboth 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 singlecharges, the current must be moving in a direction other than the directionof the field. The magnitude of the magnetic force on a current-carryingwire is found fromFB = iLB sin qwhere i is the current and L is the length of wire inthe uniform magnetic field of strength B.
1To be exact, the symbol B represents magnetic flux density,also called magnetic induction, not magnetic field. The true magneticfield is denoted by H. H and B differ only bya material-dependent constant. For most purposes, the differenceis inconsequential, so we will refer to B as the magnetic field.If you take further courses in magnetism, you will learn the distinction.

InducedCurrents, Induced EMF, and Faraday"s Law

Can you create a currentthrough a wire without connecting the wire directly to a voltage sourcelike 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 currentwill be induced in the wire. This current flows because somethingis 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 providedby a battery. A changing magnetic field through a coil of wire thereforemust induce an emf in the coil which in turn causes current to flow.The law describing induced emf is named after the British scientistMichael Faraday, but Faraday"s Law should really be called Henry"s Law.Joseph Henry, an American from the Albany area, discovered that changingmagnetic fields induced current before Faraday did. Unfortunately,he lived in the age before instantaneous electronic communication betweenEurope and America. Faraday got published and got famous before Henrycould report his findings. Interestingly enough, Henry had to explainthe results to Faraday when the two met a few years later.Briefly stated, Faraday"s law says that a changing magnetic field producesan electric field. If charges are free to move, the electric fieldwill cause an emf and a current. For example, if a loop of wire isplaced in a magnetic field so that the field passes through the loop, achange 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 areaenclosing magnetic field changes. So it is the change in magneticflux, defined asthat determines the induced current. A is the area vector;its magnitude is the area of the loop, and its direction is perpendicularto the area of the loop, and q is theangle between A and the magnetic field B. The lastequality (removing the integral) is valid only if the field is uniformover 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 movingcharges around the loop, divided by the charge. It is similar inconcept to voltage, except that no charge separation is necessary.The magnetic flux FBequals the magnetic field B times the area A of the loopwith magnetic field through it if (a) the magnetic field is perpendicularto the plane of the loop, and (b) the magnetic field is uniform throughoutthe loop. For our purposes, we will assume these two conditions aremet; in practical applications, however, magnetic field will vary througha loop, and the field will not always be perpendicular to the loop.Since all applications of Faraday"s Law to magnetic storage involvea coil of wire of fixed area, we will also assume that (c) the area doesnot change in time. We then have a simpler expression for the currentinduced in the coil:The induced current depends on both the area of the coil and the changein magnetic field. In a coil of wires, each loop contributes an areaAto the right-hand side of the equation, so the induced emf will be proportionalto the number of loops in a coil. But doubling the number of loopsdoubles the length of wire used and so doubles the resistance, so the inducedcurrent will not increase when loops are added.

Inductionand Magnetic Recording

A traditional recording head for magnetic data consists of a coil of wiresattached to some current-sensitive device. A ferromagnetic materialpasses under the coil. Such an arrangement can both write magneticdata to the ferromagnetic material and read magnetic data off of the material.To write magnetic data, current is sent through the coil in proportionto the desired signal. This current produces a magnetic field proportionalto the current. The magnetic field aligns the spins in the ferromagneticmaterial. As the material moves away from the coil, the magneticfield decreases, and the spins remain aligned until they enter anothermagnetic 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 producinga continually varying magnetic field. Digital data can be recordedby alternating the direction of the current. To minimize data lossor errors, binary data is not determined solely by the direction of magnitizationin a domain. Instead, it is represented by the change in magneticorientation between two domains. If one bit of magnetic field hasthe 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 beforeit, that represents a 1 (change). So a 1 is written by changing thedirection of current between the two domains comprising a bit, and a 0is written by keeping the direction the same. Each bit starts witha change of orientation. This convention for recording data identifieserrors, since one would never have three domains of the same orientationin a row. In addition, the orientation should change with every otherdomain. If the computer thinks a bit is complete but the orientationdoes not change, it knows that some error has occurred. Some examplesof domains, bits, and strings are shown below.To read magnetic data, the ferromagnetic material is moved past thecoil of wire. The changing magnetic field caused by the material"smotion induces a current in the coil of wire proportional to the changein field. If a 0 is represented, the magnetic field does not changebetween the two domains of a bit, so no current is induced as the magneticmaterial passes the coil. For a 1, the magnetic field changes fromone 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 ferromagneticmaterial is moved faster, the induced current is dependent on the speedof the material. Thus the sensitivity of inductive read heads islimited by the precision of the material speed. The other limitingfactor on inductive heads is the strength of the magnetic field.As efforts to increase storage density continue, the size of a data elementshrinks. Since fewer electrons are now contained in the region ofone bit, the associated magnetic field is smaller. This smaller magneticfield produces less change and thus less induced current, requiring moreloops to produce a measurable current. As mentioned above, more loopsmeans more resistance which means more heat. Because of these limitations,new magnetic storage devices use the phenomenon of magnetoresistance toread magnetic data.


FactsAbout the Force
(From Driving Force: The Natural Magic of Magnets, byJames D. Livingston, (Havard University Press: Cambridge), 1996)These 10 facts about the force from Driving Force by Livingstonsummarize most of the information contained in this and the next reading.Of particular interest to the workings of computers are steps 4, 6, and8. 9 and 10 are also important concepts to remember. This readingassignment has only touched on the applications of magnets in informationsystems and other commonly-used technologies. If you are interestedin 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 notothers (like wood or glass).
4.Magnetic forces act at a distance, and they can act through nonmagneticbarriers (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 becomesa magnet.
7.Putting iron inside a current-carrying coil greatly increases the strengthof the electromagnet.
8.Changing magnetic fields induce electric currents in copper and otherconductors.
9.A charged particle experiences no magnetic force when moving parallelto a magnetic field, but when it is moving perpendicular to the field itexperiences a force perpendicular to both the field and the direction ofmotion.
10.A current-carrying wire in a perpendicular magnetic field experiencesa force in a direction perpendicular to both the wire and the field.

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