Chapter 19Magnetism

MagnetsPoles of a magnet are the ends where objects are most strongly attractedTwo poles, called north and southLike poles repel each other and unlike poles attract each otherSimilar to electric chargesMagnetic poles cannot be isolatedIf a permanent magnetic is cut in half repeatedly, you will still have a north and a south poleThis differs from electric chargesThere is some theoretical basis for monopoles, but none have been detected

More About MagnetismAn unmagnetized piece of iron can be magnetized by stroking it with a magnetSomewhat like stroking an object to charge an objectMagnetism can be inducedIf a piece of iron, for example, is placed near a strong permanent magnet, it will become magnetized

Types of Magnetic MaterialsSoft magnetic materials, such as iron, are easily magnetizedThey also tend to lose their magnetism easilyHard magnetic materials, such as cobalt and nickel, are difficult to magnetizeThey tend to retain their magnetism

Sources of Magnetic FieldsThe region of space surrounding a moving charge includes a magnetic fieldThe charge will also be surrounded by an electric fieldA magnetic field surrounds a properly magnetized magnetic material

Magnetic FieldsA vector quantitySymbolized by Direction is given by the direction a north pole of a compass needle points in that locationMagnetic field lines can be used to show how the field lines, as traced out by a compass, would look

Magnetic Field Lines, sketchA compass can be used to show the direction of the magnetic field lines (a)A sketch of the magnetic field lines (b)

Magnetic Field Lines, Bar MagnetIron filings are used to show the pattern of the magnetic field linesThe direction of the field is the direction a north pole would point

Magnetic Field Lines, Unlike PolesIron filings are used to show the pattern of the magnetic field linesThe direction of the field is the direction a north pole would pointCompare to the magnetic field produced by an electric dipole

Magnetic Field Lines, Like PolesIron filings are used to show the pattern of the electric field linesThe direction of the field is the direction a north pole would pointCompare to the electric field produced by like charges

Earths Magnetic FieldThe Earths geographic north pole corresponds to a magnetic south poleThe Earths geographic south pole corresponds to a magnetic north poleStrictly speaking, a north pole should be a north-seeking pole and a south pole a south-seeking pole

Earths Magnetic FieldThe Earths magnetic field resembles that achieved by burying a huge bar magnet deep in the Earths interior

Dip Angle of Earths Magnetic FieldIf a compass is free to rotate vertically as well as horizontally, it points to the earths surfaceThe angle between the horizontal and the direction of the magnetic field is called the dip angleThe farther north the device is moved, the farther from horizontal the compass needle would beThe compass needle would be horizontal at the equator and the dip angle would be 0The compass needle would point straight down at the south magnetic pole and the dip angle would be 90

More About the Earths Magnetic PolesThe dip angle of 90 is found at a point just north of Hudson Bay in CanadaThis is considered to be the location of the south magnetic poleThe magnetic and geographic poles are not in the same exact locationThe difference between true north, at the geographic north pole, and magnetic north is called the magnetic declinationThe amount of declination varies by location on the earths surface

Earths Magnetic Declination

Source of the Earths Magnetic FieldThere cannot be large masses of permanently magnetized materials since the high temperatures of the core prevent materials from retaining permanent magnetizationThe most likely source of the Earths magnetic field is believed to be electric currents in the liquid part of the core

Reversals of the Earths Magnetic FieldThe direction of the Earths magnetic field reverses every few million yearsEvidence of these reversals are found in basalts resulting from volcanic activityThe origin of the reversals is not understood

Magnetic FieldsWhen moving through a magnetic field, a charged particle experiences a magnetic forceThis force has a maximum value when the charge moves perpendicularly to the magnetic field linesThis force is zero when the charge moves along the field lines

Magnetic Fields, contOne can define a magnetic field in terms of the magnetic force exerted on a test charge moving in the field with velocity Similar to the way electric fields are defined

Units of Magnetic FieldThe SI unit of magnetic field is the Tesla (T)

Wb is a WeberThe cgs unit is a Gauss (G)1 T = 104 G

A Few Typical B ValuesConventional laboratory magnets25000 G or 2.5 TSuperconducting magnets300000 G or 30 TEarths magnetic field0.5 G or 5 x 10-5 T

Finding the Direction of Magnetic ForceExperiments show that the direction of the magnetic force is always perpendicular to both and Fmax occurs when is perpendicular toF = 0 when is parallel to

Right Hand Rule #1Place your fingers in the direction of Curl the fingers in the direction of the magnetic field, Your thumb points in the direction of the force, , on a positive charge If the charge is negative, the force is opposite that determined by the right hand rule

Magnetic Force on a Current Carrying ConductorA force is exerted on a current-carrying wire placed in a magnetic fieldThe current is a collection of many charged particles in motionThe direction of the force is given by right hand rule #1

Force on a WireThe blue xs indicate the magnetic field is directed into the pageThe x represents the tail of the arrowBlue dots would be used to represent the field directed out of the pageThe represents the head of the arrowIn this case, there is no current, so there is no force

Force on a Wire,contB is into the pageThe current is up the pageThe force is to the left

Force on a Wire,finalB is into the pageThe current is down the pageThe force is to the right

Force on a Wire, equationThe magnetic force is exerted on each moving charge in the wireThe total force is the sum of all the magnetic forces on all the individual charges producing the currentF = B I sin is the angle between and the direction of IThe direction is found by the right hand rule, placing your fingers in the direction of I instead of

Torque on a Current Loop Applies to any shape loopN is the number of turns in the coil Torque has a maximum value of NBIAWhen q = 90Torque is zero when the field is parallel to the plane of the loop

Magnetic MomentThe vector is called the magnetic moment of the coilIts magnitude is given by m = IANThe vector always points perpendicular to the plane of the loop(s)The angle is between the moment and the fieldThe equation for the magnetic torque can be written as t = mB sinq

Electric MotorAn electric motor converts electrical energy to mechanical energyThe mechanical energy is in the form of rotational kinetic energyAn electric motor consists of a rigid current-carrying loop that rotates when placed in a magnetic field

Electric Motor, 2The torque acting on the loop will tend to rotate the loop to smaller values of until the torque becomes 0 at = 0If the loop turns past this point and the current remains in the same direction, the torque reverses and turns the loop in the opposite direction

Electric Motor, 3To provide continuous rotation in one direction, the current in the loop must periodically reverseIn ac motors, this reversal naturally occursIn dc motors, a split-ring commutator and brushes are usedActual motors would contain many current loops and commutators

Electric Motor, finalJust as the loop becomes perpendicular to the magnetic field and the torque becomes 0, inertia carries the loop forward and the brushes cross the gaps in the ring, causing the current loop to reverse its directionThis provides more torque to continue the rotationThe process repeats itself

Force on a Charged Particle in a Magnetic FieldConsider a particle moving in an external magnetic field so that its velocity is perpendicular to the fieldThe force is always directed toward the center of the circular pathThe magnetic force causes a centripetal acceleration, changing the direction of the velocity of the particle

Force on a Charged ParticleEquating the magnetic and centripetal forces:

Solving for r:

r is proportional to the momentum of the particle and inversely proportional to the magnetic fieldSometimes called the cyclotron equation

Particle Moving in an External Magnetic FieldIf the particles velocity is not perpendicular to the field, the path followed by the particle is a spiralThe spiral path is called a helix

Hans Christian Oersted1777 1851Best known for observing that a compass needle deflects when placed near a wire carrying a currentFirst evidence of a connection between electric and magnetic phenomena

Magnetic Fields Long Straight WireA current-carrying wire produces a magnetic fieldThe compass needle deflects in directions tangent to the circleThe compass needle points in the direction of the magnetic field produced by the current

Direction of the Field of a Long Straight WireRight Hand Rule #2Grasp the wire in your right handPoint your thumb in the direction of the currentYour fingers will curl in the direction of the field

Magnitude of the Field of a Long Straight WireThe magnitude of the field at a distance r from a wire carrying a current of I is

o = 4 x 10-7 T.m / Ao is called the permeability of free space

Ampres LawAndr-Marie Ampre found a procedure for deriving the relationship between the current in an arbitrarily shaped wire and the magnetic field produced by the wireAmpres Circuital LawB|| = o ISum over the closed path

Ampres Law, contChoose an arbitrary closed path around the currentSum all the products of B|| around the closed path

Ampres Law to Find B for a Long Straight WireUse a closed circular pathThe circumference of the circle is 2 r

This is identical to the result previously obtained

Andr-Marie Ampre1775 1836Credited with the discovery of electromagnetismRelationship between electric currents and magnetic fieldsMathematical genius evident by age 12

Magnetic Force Between Two Parallel ConductorsThe force on wire 1 is due to the current in wire 1 and the magnetic field produced by wire 2The force per unit length is:

Force Between Two Conductors, contParallel conductors carrying currents in the same direction attract each other Parallel conductors carrying currents in the opposite directions repel each other

Defining Ampere and CoulombThe force between parallel conductors can be used to define the Ampere (A)If two long, parallel wires 1 m apart carry the same current, and the magnitude of the magnetic force per unit length is 2 x 10-7 N/m, then the current is defined to be 1 AThe SI unit of charge, the Coulomb (C), can be defined in terms of the AmpereIf a conductor carries a steady current of 1 A, then the quantity of charge that flows through any cross section in 1 second is 1 C

Magnetic Field of a Current LoopThe strength of a magnetic field produced by a wire can be enhanced by forming the wire into a loopAll the segments, x, contribute to the field, increasing its strength

Magnetic Field of a Current Loop Total Field

Magnetic Field of a Current Loop EquationThe magnitude of the magnetic field at the center of a circular loop with a radius R and carrying current I is

With N loops in the coil, this becomes

Magnetic Field of a SolenoidIf a long straight wire is bent into a coil of several closely spaced loops, the resulting device is called a solenoidIt is also known as an electromagnet since it acts like a magnet only when it carries a current

Magnetic Field of a Solenoid, 2The field lines inside the solenoid are nearly parallel, uniformly spaced, and close togetherThis indicates that the field inside the solenoid is nearly uniform and strongThe exterior field is nonuniform, much weaker, and in the opposite direction to the field inside the solenoid

Magnetic Field in a Solenoid, 3The field lines of the solenoid resemble those of a bar magnet

Magnetic Field in a Solenoid, MagnitudeThe magnitude of the field inside a solenoid is constant at all points far from its endsB = o n In is the number of turns per unit lengthn = N / The same result can be obtained by applying Ampres Law to the solenoid

Magnetic Field in a Solenoid from Ampres LawA cross-sectional view of a tightly wound solenoidIf the solenoid is long compared to its radius, we assume the field inside is uniform and outside is zeroApply Ampres Law to the blue dashed rectangle

Magnetic Effects of Electrons Orbits An individual atom should act like a magnet because of the motion of the electrons about the nucleusEach electron circles the atom once in about every 10-16 secondsThis would produce a current of 1.6 mA and a magnetic field of about 20 T at the center of the circular pathHowever, the magnetic field produced by one electron in an atom is often canceled by an oppositely revolving electron in the same atom

Magnetic Effects of Electrons Orbits, contThe net result is that the magnetic effect produced by electrons orbiting the nucleus is either zero or very small for most materials

Magnetic Effects of Electrons Spins Electrons also have spinThe classical model is to consider the electrons to spin like topsIt is actually a quantum effect

Magnetic Effects of Electrons Spins, contThe field due to the spinning is generally stronger than the field due to the orbital motionElectrons usually pair up with their spins opposite each other, so their fields cancel each otherThat is why most materials are not naturally magnetic

Magnetic Effects of Electrons Domains In some materials, the spins do not naturally cancelSuch materials are called ferromagneticLarge groups of atoms in which the spins are aligned are called domainsWhen an external field is applied, the domains that are aligned with the field tend to grow at the expense of the othersThis causes the material to become magnetized

Domains, contRandom alignment, a, shows an unmagnetized materialWhen an external field is applied, the domains aligned with B grow, b

Domains and Permanent MagnetsIn hard magnetic materials, the domains remain aligned after the external field is removedThe result is a permanent magnetIn soft magnetic materials, once the external field is removed, thermal agitation causes the materials to quickly return to an unmagnetized stateWith a core in a loop, the magnetic field is enhanced since the domains in the core material align, increasing the magnetic field