Chapter 32 Lecture Physics
4/7/2016Chapter 32 LecturephysicsFOR SCIENTISTS AND ENGINEERSa strategic approachTHIRD EDITIONrandall d. knight 2013 Pearson Education, Inc.Chapter 32 The Magnetic FieldChapter Goal: To learn how to calculate and usethe magnetic field. 2013 Pearson Education, Inc.Slide 32-2Chapter 32 Preview 2013 Pearson Education, Inc.Slide 32-31
4/7/2016Chapter 32 Preview 2013 Pearson Education, Inc.Slide 32-4Chapter 32 Preview 2013 Pearson Education, Inc.Slide 32-5Chapter 32 Preview 2013 Pearson Education, Inc.Slide 32-62
4/7/2016Chapter 32 PreviewSlide 32-7 2013 Pearson Education, Inc.Chapter 32 PreviewSlide 32-8 2013 Pearson Education, Inc.Chapter 32 Reading Quiz 2013 Pearson Education, Inc.Slide 32-93
4/7/2016Reading Question 32.1What is the SI unit for the strength of the l.Bohr magneton. 2013 Pearson Education, Inc.Slide 32-10Reading Question 32.1What is the SI unit for the strength of the l.Bohr magneton. 2013 Pearson Education, Inc.Slide 32-11Reading Question 32.2What is the shape of the trajectory that a chargedparticle follows in a uniform magnetic rbola. 2013 Pearson Education, Inc.Slide 32-124
4/7/2016Reading Question 32.2What is the shape of the trajectory that a chargedparticle follows in a uniform magnetic rbola. 2013 Pearson Education, Inc.Slide 32-13Reading Question 32.3The magnetic field of a point charge is given byA. Biot-Savart’s law.B. Faraday’s law.C. Gauss’s law.D. Ampère’s law.E. Einstein’s law. 2013 Pearson Education, Inc.Slide 32-14Reading Question 32.3The magnetic field of a point charge is given byA. Biot-Savart’s law.B. Faraday’s law.C. Gauss’s law.D. Ampère’s law.E. Einstein’s law. 2013 Pearson Education, Inc.Slide 32-155
4/7/2016Reading Question 32.4The magnetic field of a straight, current-carryingwire isA.B.C.D.E.Parallel to the wire.Inside the wire.Perpendicular to the wire.Around the wire.Zero. 2013 Pearson Education, Inc.Slide 32-16Reading Question 32.4The magnetic field of a straight, current-carryingwire isA.B.C.D.E.Parallel to the wire.Inside the wire.Perpendicular to the wire.Around the wire.Zero. 2013 Pearson Education, Inc.Slide 32-17Chapter 32 Content, Examples, andQuickCheck Questions 2013 Pearson Education, Inc.Slide 32-186
4/7/2016Discovering Magnetism: Experiment 1Tape a bar magnet to apiece of cork and allow itto float in a dish of water.It always turns to alignitself in an approximatenorth-south direction.The end of a magnet that points north is called thenorth-seeking pole, or simply the north pole.The end of a magnet that points south is called thesouth pole. 2013 Pearson Education, Inc.Slide 32-19Discovering Magnetism: Experiment 2If the north pole of one magnet is brought near thenorth pole of another magnet, they repel each other.Two south poles also repel each other, but the northpole of one magnet exerts an attractive force on thesouth pole of another magnet. 2013 Pearson Education, Inc.Slide 32-20Discovering Magnetism: Experiment 3The north pole of a bar magnet attracts one end of acompass needle and repels the other.Apparently the compass needle itself is a little barmagnet with a north pole and a south pole. 2013 Pearson Education, Inc.Slide 32-217
4/7/2016Discovering Magnetism: Experiment 4Cutting a bar magnet in half produces two weaker butstill complete magnets, each with a north pole and asouth pole.No matter how small the magnets are cut, even downto microscopic sizes, each piece remains a completemagnet with two poles.Slide 32-22 2013 Pearson Education, Inc.Discovering Magnetism: Experiment 5Magnets can pick up someobjects, such as paper clips,but not all.If an object is attracted to oneend of a magnet, it is alsoattracted to the other end.Most materials, includingcopper (a penny), aluminum,glass, and plastic, experienceno force from a magnet. 2013 Pearson Education, Inc.Slide 32-23Discovering Magnetism: Experiment 6A magnet does not affect anelectroscope.A charged rod exerts a weakattractive force on both endsof a magnet.However, the force is thesame as the force on a metalbar that isn’t a magnet, so itis simply a polarization forcelike the ones we studied inChapter 25.Other than polarization forces, charges have no effects onmagnets. 2013 Pearson Education, Inc.Slide 32-248
4/7/2016What Do These Experiments Tell Us?1. Magnetism is not the same as electricity.2. Magnetism is a long range force.3. All magnets have two poles, called north and southpoles. Two like poles exert repulsive forces on eachother; two opposite poles attract.4. The poles of a bar magnet can be identified by usingit as a compass. The north pole tends to rotate topoint approximately north.5. Materials that are attracted to a magnet are calledmagnetic materials. The most common magneticmaterial is iron. 2013 Pearson Education, Inc.Slide 32-25QuickCheck 32.1If the bar magnet is flipped over and the south pole isbrought near the hanging ball, the ball will beA. Attracted to themagnet.B. Repelled by themagnet.C. Unaffected bythe magnet.D. I’m not sure. 2013 Pearson Education, Inc.Slide 32-26QuickCheck 32.1If the bar magnet is flipped over and the south pole isbrought near the hanging ball, the ball will beA. Attracted to themagnet.B. Repelled by themagnet.C. Unaffected bythe magnet.D. I’m not sure. 2013 Pearson Education, Inc.Slide 32-279
4/7/2016QuickCheck 32.2The compass needle can rotate on a pivot in a horizontalplane. If a positively charged rod is brought near, asshown, the compass needle willA. Rotate clockwise.B. Rotatecounterclockwise.C. Do nothing.D. I’m not sure. 2013 Pearson Education, Inc.Slide 32-28QuickCheck 32.2The compass needle can rotate on a pivot in a horizontalplane. If a positively charged rod is brought near, asshown, the compass needle willA. Rotate clockwise.B. Rotatecounterclockwise.C. Do nothing.Magnetic poles are not the sameas electric charges.D. I’m not sure. 2013 Pearson Education, Inc.Slide 32-29QuickCheck 32.3If a bar magnet is cut in half, you end up with 2013 Pearson Education, Inc.Slide 32-3010
4/7/2016QuickCheck 32.3If a bar magnet is cut in half, you end up with 2013 Pearson Education, Inc.Slide 32-31Compasses and GeomagnetismDue to currents inthe molten iron core,the earth itself actsas a large magnet.The poles are slightlyoffset from the polesof the rotation axis.The geographic northpole is actually asouth magnetic pole! 2013 Pearson Education, Inc.Slide 32-32Electric Current Causes a Magnetic FieldIn 1819 Hans Christian Oersted discovered that anelectric current in a wire causes a compass to turn. 2013 Pearson Education, Inc.Slide 32-3311
4/7/2016Electric Current Causes a Magnetic FieldThe right-hand rule determines the orientation ofthe compass needles to the direction of the current. 2013 Pearson Education, Inc.Slide 32-34Electric Current Causes a Magnetic FieldThe magnetic field is revealed by the pattern of ironfilings around a current-carrying wire. 2013 Pearson Education, Inc.Slide 32-35Notation for Vectors and Currents Perpendicularto the PageMagnetism requires a three-dimensional perspective,but two-dimensional figures are easier to draw.We will use the following notation: 2013 Pearson Education, Inc.Slide 32-3612
4/7/2016Electric Current Causes a Magnetic FieldThe right-hand rule determines the orientation ofthe compass needles to the direction of the current.Slide 32-37 2013 Pearson Education, Inc.QuickCheck 32.4A long, straight wire extends into and out of thescreen. The current in the wire isA. Into the screen.B. Out of the screen.C. There is no currentin the wire.D. Not enough info totell the direction.Slide 32-38 2013 Pearson Education, Inc.QuickCheck 32.4A long, straight wire extends into and out of thescreen. The current in the wire isA. Into the screen.B. Out of the screen.C. There is no currentin the wire.D. Not enough info totell the direction. 2013 Pearson Education, Inc.Right-hand ruleSlide 32-3913
4/7/2016Magnetic Force on a CompassThe figure shows a compassneedle in a magnetic field.A magnetic force is exertedon each of the two poles ofthe compass, parallel to forthe north pole and oppositefor the south pole.This pair of opposite forcesexerts a torque on theneedle, rotating the needleuntil it is parallel to themagnetic field at that point.Slide 32-40 2013 Pearson Education, Inc.Electric Current Causes a Magnetic FieldBecause compass needlesalign with the magneticfield, the magnetic field ateach point must be tangentto a circle around the wire.The figure shows themagnetic field by drawingfield vectors.Notice that the field isweaker (shorter vectors) atgreater distances from thewire.Slide 32-41 2013 Pearson Education, Inc.Electric Current Causes a Magnetic FieldMagnetic field lines areimaginary lines drawn througha region of space so that:A tangent to a field line is inthe direction of the magneticfield.The field lines are closertogether where the magneticfield strength is larger. 2013 Pearson Education, Inc.Slide 32-4214
4/7/2016Tactics: Right-Hand Rule for FieldsSlide 32-43 2013 Pearson Education, Inc.The Source of the Magnetic Field: MovingChargesThe magnetic field of acharged particle q movingwith velocity v is given bythe Biot-Savart law:Slide 32-44 2013 Pearson Education, Inc.The Magnetic FieldThe constant µ0 in the Biot-Savart law is called thepermeability constant:µ0 4π 10-7 Tm/A 1.257 10-6 Tm/AThe SI unit of magneticfield strength is thetesla, abbreviated as T:1 tesla 1 T 1 N/A m 2013 Pearson Education, Inc.Slide 32-4515
4/7/2016Magnetic Field of a Moving Positive ChargeThe right-hand rule for findingthe direction of due to amoving positive charge issimilar to the rule used for acurrent carrying wire.Note that the component ofparallel to the line of motion iszero. 2013 Pearson Education, Inc.Slide 32-46Example 32.1 The Magnetic Field of a Proton 2013 Pearson Education, Inc.Slide 32-47Example 32.1 The Magnetic Field of a Proton 2013 Pearson Education, Inc.Slide 32-4816
4/7/2016Example 32.1 The Magnetic Field of a Proton 2013 Pearson Education, Inc.Slide 32-49Example 32.1 The Magnetic Field of a Proton 2013 Pearson Education, Inc.Slide 32-50Superposition of Magnetic FieldsMagnetic fields, like electric fields, have been foundexperimentally to obey the principle of superposition.If there are n moving point charges, the net magneticfield is given by the vector sum:The principle of superposition will be the basis forcalculating the magnetic fields of several importantcurrent distributions. 2013 Pearson Education, Inc.Slide 32-5117
4/7/2016The Cross Product (CD sin α, direction given by the right-hand rule) 2013 Pearson Education, Inc.Slide 32-52Magnetic Field of a Moving ChargeThe magnetic field of a charged particle q moving withvelocity is given by the Biot-Savart law: 2013 Pearson Education, Inc.Slide 32-53QuickCheck 32.5What is the direction of the magnetic field at theposition of the dot?A.B.C.D.E.Into the screen.Out of the screen.Up.Down.Left. 2013 Pearson Education, Inc.Slide 32-5418
4/7/2016QuickCheck 32.5What is the direction of the magnetic field at theposition of the dot?A.B.C.D.E.Into the screen.Out of the screen.Up.Down.Left. 2013 Pearson Education, Inc.Slide 32-55Example 32.2 The Magnetic Field Direction of aMoving Electron 2013 Pearson Education, Inc.Slide 32-56The Magnetic Field of a CurrentThe figure shows a currentcarrying wire.The wire as a whole is electrically neutral, butcurrent I represents the motion of positivecharge carriers through the wire. 2013 Pearson Education, Inc.Slide 32-5719
4/7/2016The Magnetic Field of a Current 2013 Pearson Education, Inc.Slide 32-58The Magnetic Field of a CurrentThe magnetic field of a long, straight wire carrying currentI at a distance d from the wire is:The magnetic field at the center of a coil of N turnsand radius R, carrying a current I is: 2013 Pearson Education, Inc.Slide 32-59QuickCheck 32.6Compared to the magnetic field at point A, the magneticfield at point B isA. Half as strong, same direction.B. Half as strong, opposite direction.C. One-quarter as strong, samedirection.D. One-quarter as strong, oppositedirection.E. Can’t compare without knowing I. 2013 Pearson Education, Inc.Slide 32-6020
4/7/2016QuickCheck 32.6Compared to the magnetic field at point A, the magneticfield at point B isA. Half as strong, same direction.B. Half as strong, opposite direction.C. One-quarter as strong, samedirection.D. One-quarter as strong, oppositedirection.E. Can’t compare without knowing I. 2013 Pearson Education, Inc.Slide 32-61Problem-Solving Strategy: The Magnetic Field ofa Current 2013 Pearson Education, Inc.Slide 32-62Problem-Solving Strategy: The Magnetic Field ofa Current 2013 Pearson Education, Inc.Slide 32-6321
4/7/2016Example 32.4 The Magnetic Field Strength Neara Heater Wire 2013 Pearson Education, Inc.Slide 32-64Example 32.4 The Magnetic Field Strength Neara Heater Wire 2013 Pearson Education, Inc.Slide 32-65Example 32.4 The Magnetic Field Strength Neara Heater Wire 2013 Pearson Education, Inc.Slide 32-6622
4/7/2016Example 32.6 Matching the Earth’s MagneticField 2013 Pearson Education, Inc.Slide 32-67Example 32.6 Matching the Earth’s MagneticField 2013 Pearson Education, Inc.Slide 32-68Example 32.6 Matching the Earth’s MagneticField 2013 Pearson Education, Inc.Slide 32-6923
4/7/2016The Magnetic Field of a Current Loop 2013 Pearson Education, Inc.Slide 32-70The Magnetic Field of a Current LoopThe magnetic field is revealed by the pattern of ironfilings around a current-carrying loop of wire. 2013 Pearson Education, Inc.Slide 32-71QuickCheck 32.7The magnet field at point P isA. Into the screen.B. Out of the screen.C. Zero. 2013 Pearson Education, Inc.Slide 32-7224
4/7/2016QuickCheck 32.7The magnet field at point P isA. Into the screen.B. Out of the screen.C. Zero. 2013 Pearson Education, Inc.Slide 32-73Tactics: Finding the Magnetic Field Direction of aCurrent Loop 2013 Pearson Education, Inc.Slide 32-74A Current Loop Is a Magnetic Dipole 2013 Pearson Education, Inc.Slide 32-7525
4/7/2016QuickCheck 32.8Where is the north magnetic pole of this current loop?A.B.C.D.E.Top side.Bottom side.Right side.Left side.Current loops don’thave north poles. 2013 Pearson Education, Inc.Slide 32-76QuickCheck 32.8Where is the north magnetic pole of this current loop?A.B.C.D.E.Top side.Bottom side.Right side.Left side.Current loops don’thave north poles. 2013 Pearson Education, Inc.Slide 32-77The Magnetic Dipole MomentThe magnetic dipole moment of a current loopenclosing an area A is defined as: 2013 Pearson Education, Inc.Slide 32-7826
4/7/2016The Magnetic Dipole MomentThe SI units of the magnetic dipole moment are A m2.The on-axis field of a magnetic dipole is: 2013 Pearson Education, Inc.Slide 32-79QuickCheck 32.9What is the current direction in the loop?A. Out at the top, in at thebottom.B. In at the top, out at thebottom.C. Either A or B wouldcause the current loopand the bar magnet torepel each other. 2013 Pearson Education, Inc.Slide 32-80QuickCheck 32.9What is the current direction in the loop?A. Out at the top, in at thebottom.B. In at the top, out at thebottom.C. Either A or B wouldcause the current loopand the bar magnet torepel each other. 2013 Pearson Education, Inc.Slide 32-8127
4/7/2016Line IntegralsFigure (a) shows acurved line from i to f.The length l of this linecan be found by doinga line integral:Slide 32-82 2013 Pearson Education, Inc.Line IntegralsFigure (a) shows acurved line whichpasses through amagnetic field B .We can find the lineintegral of B from i to fas measured along thisline, in this direction: 2013 Pearson Education, Inc.Slide 32-83Tactics: Evaluating Line Integrals 2013 Pearson Education, Inc.Slide 32-8428
4/7/2016Ampère’s LawConsider a lineintegral of Bevaluated along acircular path all theway around a wirecarrying current I.This is the lineintegral around aclosed curve, whichis denoted: 2013 Pearson Education, Inc.Slide 32-85Ampère’s LawBecause B is tangentto the circle and ofconstant magnitudeat every point on thecircle, we can write:Here B µ0I/2πd,where I is the currentthrough this loop,hence: 2013 Pearson Education, Inc.Slide 32-86Ampère’s LawWhenever total currentIthrough passes throughan area bounded by aclosed curve, the lineintegral of themagnetic field aroundthe curve is given byAmpère’s law: 2013 Pearson Education, Inc.Slide 32-8729
4/7/2016QuickCheck 32.10The line integral of B around the loop is µ0 · 7.0 A.Current I3 isA.B.C.D.E.0 A.1 A out of the screen.1 A into the screen.5 A out of the screen.5 A into the screen. 2013 Pearson Education, Inc.Slide 32-88QuickCheck 32.10The line integral of B around the loop is µ0 · 7.0 A.Current I3 isA.B.C.D.E.0 A.1 A out of the screen.1 A into the screen.5 A out of the screen.5 A into the screen. 2013 Pearson Education, Inc.Slide 32-89QuickCheck 32.11For the path shown,A.B.C.D.0.µ0(I1 I2).µ0(I2 I1).µ0(I1 I2). 2013 Pearson Education, Inc.Slide 32-9030
4/7/2016QuickCheck 32.11For the path shown,A.B.C.D.0.µ0(I1 I2).µ0(I2 I1).µ0(I1 I2).Slide 32-91 2013 Pearson Education, Inc.SolenoidsA uniform magnetic field canbe generated with a solenoid.A solenoid is a helical coil ofwire with the same current Ipassing through each loop inthe coil.Solenoids may have hundredsor thousands of coils, oftencalled turns, sometimeswrapped in several layers.The magnetic field isstrongest and most uniforminside the solenoid. 2013 Pearson Education, Inc.Slide 32-92The Magnetic Field of a SolenoidWith many current loops along the same axis, the field inthe center is strong and roughly parallel to the axis,whereas the field outside the loops is very close to zero. 2013 Pearson Education, Inc.Slide 32-9331
4/7/2016The Magnetic Field of a SolenoidNo real solenoid is ideal, but a very uniform magneticfield can be produced near the center of a tightly woundsolenoid whose length is much larger than its diameter.Slide 32-94 2013 Pearson Education, Inc.The Magnetic Field of a SolenoidThe figure shows a crosssection through an infinitelylong solenoid.The integration path thatwe’ll use is a rectangle.The current passingthrough this rectangle isIthrough NI.Ampère’s Law is thus:µ0Ithrough µ0NISlide 32-95 2013 Pearson Education, Inc.The Magnetic Field of a SolenoidAlong the top, the line integralis zero since B 0 outside thesolenoid.Along the sides, the lineintegral is zero since the fieldis perpendicular to the path.Along the bottom, the lineintegral is simply Bl.Solving for B inside thesolenoid:where n N/l is the numberof turns per unit length. 2013 Pearson Education, Inc.Slide 32-9632
4/7/2016QuickCheck 32.12Solenoid 2 has twice the diameter, twice the length, andtwice as many turns as solenoid 1. How does the field B2at the center of solenoid 2 compare to B1 at the center ofsolenoid 1?A.B.C.D.E.B2 B1/4.B2 B1/2.B2 B1 .B2 2B1.B2 4B1.Slide 32-97 2013 Pearson Education, Inc.QuickCheck 32.12Solenoid 2 has twice the diameter, twice the length, andtwice as many turns as solenoid 1. How does the field B2at the center of solenoid 2 compare to B1 at the center ofsolenoid 1?A.B.C.D.E.B2 B1/4.B2 B1/2.B2 B1 .B2 2B1.B2 4B1.Same turns-per-length 2013 Pearson Education, Inc.Slide 32-98QuickCheck 32.13The current in this solenoidA. Enters on the left,leaves on the right.B. Enters on the right,leaves on the left.C. Either A or B wouldproduce this field. 2013 Pearson Education, Inc.Slide 32-9933
4/7/2016QuickCheck 32.13The current in this solenoidA. Enters on the left,leaves on the right.B. Enters on the right,leaves on the left.C. Either A or B wouldproduce this field. 2013 Pearson Education, Inc.Slide 32-100Generating an MRI Magnetic FieldThis patient is undergoing magnetic resonance imaging (MRI).The large cylinder surrounding the patient contains a solenoidthat is wound with superconducting wire to generate a stronguniform magnetic field. 2013 Pearson Education, Inc.Slide 32-101Example 32.9 Generating an MRI Magnetic Field 2013 Pearson Education, Inc.Slide 32-10234
4/7/2016Example 32.9 Generating an MRI Magnetic Field 2013 Pearson Education, Inc.Slide 32-103Example 32.9 Generating an MRI Magnetic Field 2013 Pearson Education, Inc.Slide 32-104The Magnetic Field Outside a SolenoidThe magnetic field outside a solenoid looks like thatof a bar magnet.Thus a solenoid is an electromagnet, and you canuse the right-hand rule to identify the north-pole end. 2013 Pearson Education, Inc.Slide 32-10535
4/7/2016Ampère’s ExperimentAfter the discovery thatelectric current producesa magnetic field, Ampèreset up two parallel wiresthat could carry largecurrents either in thesame direction or inopposite directions.Ampère’s experimentshowed that a magneticfield exerts a force on acurrent. 2013 Pearson Education, Inc.Slide 32-106The Magnetic Force on a Moving ChargeThe magnetic force turns out to depend not only onthe charge and the charge’s velocity, but also onhow the velocity vector is oriented relative to themagnetic field. 2013 Pearson Education, Inc.Slide 32-107The Magnetic Force on a Moving ChargeThe magnetic force turns out to depend not only onthe charge and the charge’s velocity, but also onhow the velocity vector is oriented relative to themagnetic field. 2013 Pearson Education, Inc.Slide 32-10836
4/7/2016The Magnetic Force on a Moving ChargeThe magnetic force turns out to depend not only onthe charge and the charge’s velocity, but also onhow the velocity vector is oriented relative to themagnetic field. 2013 Pearson Education, Inc.Slide 32-109The Magnetic Force on a Moving ChargeThe magnetic force on a charge q as it movesthrough a magnetic field B with velocity v is:where α is the angle between v and B. 2013 Pearson Education, Inc.Slide 32-110The Magnetic Force on a Moving Charge 2013 Pearson Education, Inc.Slide 32-11137
4/7/2016QuickCheck 32.14The direction of the magnetic force on the proton isA.B.C.D.E.To the right.To the left.Into the screen.Out of the screen.The magnetic forceis zero. 2013 Pearson Education, Inc.Slide 32-112QuickCheck 32.14The direction of the magnetic force on the proton isA.B.C.D.E.To the right.To the left.Into the screen.Out of the screen.The magnetic forceis zero. 2013 Pearson Education, Inc.Slide 32-113QuickCheck 32.15The direction of the magnetic force on the electron isA.B.C.D.E.Upward.Downward.Into the screen.Out of the screen.The magnetic forceis zero. 2013 Pearson Education, Inc.Slide 32-11438
4/7/2016QuickCheck 32.15The direction of the magnetic force on the electron isA.B.C.D.E.Upward.Downward.Into the screen.Out of the screen.The magnetic forceis zero. 2013 Pearson Education, Inc.Slide 32-115QuickCheck 32.16Which magnetic field causes the observed force? 2013 Pearson Education, Inc.Slide 32-116QuickCheck 32.16Which magnetic field causes the observed force? 2013 Pearson Education, Inc.Slide 32-11739
4/7/2016Example 32.10 The Magnetic Force on anElectron 2013 Pearson Education, Inc.Slide 32-118Example 32.10 The Magnetic Force on anElectron 2013 Pearson Education, Inc.Slide 32-119Example 32.10 The Magnetic Force on anElectron 2013 Pearson Education, Inc.Slide 32-12040
4/7/2016Example 32.10 The Magnetic Force on anElectron 2013 Pearson Education, Inc.Slide 32-121QuickCheck 32.17Which magnetic field (if it’s the correct strength) allowsthe electron to pass through the charged electrodeswithout being deflected? 2013 Pearson Education, Inc.Slide 32-122QuickCheck 32.17Which magnetic field (if it’s the correct strength) allowsthe electron to pass through the charged electrodeswithout being deflected? 2013 Pearson Education, Inc.Slide 32-12341
4/7/2016QuickCheck 32.18A proton is shot straight at the center of a long, straightwire carrying current into the screen. The proton willA. Go straight into thewire.B. Hit the wire in frontof the screen.C. Hit the wire behindthe screen.D. Be deflected overthe wire.E. Be deflected underthe wire. 2013 Pearson Education, Inc.Slide 32-124QuickCheck 32.18A proton is shot straight at the center of a long, straightwire carrying current into the screen. The proton willA. Go straight into thewire.B. Hit the wire in frontof the screen. v B points out of the screenC. Hit the wire behindthe screen.D. Be deflected overthe wire.E. Be deflected underthe wire. 2013 Pearson Education, Inc.Slide 32-125Cyclotron MotionThe figure shows a positivecharge moving in a planethat is perpendicular to auniform magnetic field.Since is alwaysperpendicular to , thecharge undergoes uniformcircular motion.This motion is called thecyclotron motion of acharged particle in amagnetic field. 2013 Pearson Education, Inc.Slide 32-12642
4/7/2016Cyclotron MotionElectrons undergoing circular cyclotron motion in amagnetic field. You can see the electrons’ path becausethey collide with a low density gas that then emits light.Slide 32-127 2013 Pearson Education, Inc.Cyclotron MotionConsider a particle with mass m and charge q movingwith a speed v in a plane that is perpendicular to auniform magnetic field of strength B.Newton’s second law for circular motion, which youlearned in Chapter 8, is:The radius of the cyclotron orbit is:Recall that the frequency of revolution of circular motionis f v/2πr, so the cyclotron frequency is: 2013 Pearson Education, Inc.Slide 32-128Cyclotron MotionThe figure shows a more generalsituation in which the chargedparticle’s velocity is not exactlyperpendicular to .The component of parallel tois not affected by the field, so thecharged particle spirals aroundthe magnetic field lines in ahelical trajectory.The radius of the helix isdetermined by v , the componentof perpendicular to . 2013 Pearson Education, Inc.Slide 32-12943
4/7/2016Aurora 2013 Pearson Education, Inc.Slide 32-130The CyclotronThe first practicalparticle accelerator,invented in the1930s, was thecyclotron.Cyclotrons remainimportant for manyapplications ofnuclear physics, suchas the creation ofradioisotopes formedicine. 2013 Pearson Education, Inc.Slide 32-131The Hall EffectConsider a magnetic field perpendicular to a flat, currentcarrying conductor.As the charge carriers move at the drift speed vd, they willexperience a magnetic force FB evdB perpendicular toboth and the current I. 2013 Pearson Education, Inc.Slide 32-13244
4/7/2016The Hall EffectIf the charge carriers are positive, the magnetic forcepushes these positive charges down, creating anexcess positive charge on the bottom surface, andleaving negative charge on the top.This creates a measureable Hall voltage VH which ishigher on the bottom surface . 2013 Pearson Education, Inc.Slide 32-133The Hall EffectIf the charge carriers are negative, the magnetic forcepushes these positive charges down, creating anexcess negative charge on the bottom surface, andleaving positive charge on the top.This creates a measureable Hall voltage VH which ishigher on the top surface. 2013 Pearson Education, Inc.Slide 32-134The Hall EffectWhen charges are separated by a magnetic field in arectangular conductor of thickness t and width w, itcreates an electric field E VH/w inside the conductor.The steady-state condition is when the electric forcebalances the magnetic force, FB FE:where vd is the drift speed, which is vd I/(wtne).From this we can find the Hall voltage:where n is the charge-carrier density (charge carriersper m3). 2013 Pearson Education, Inc.Slide 32-13545
4/7/2016Example 32.12 Measuring the Magnetic Field 2013 Pearson Education, Inc.Slide 32-136Example 32.12 Measuring the Magnetic Field 2013 Pearson Education, Inc.Slide 32-137Example 32.12 Measuring the Magnetic Field 2013 Pearson Education, Inc.Slide 32-13846
4/7/2016Magnetic Forces on Current-Carrying WiresThere’s no force on a currentcarrying wire parallel to amagnetic field.Slide 32-139 2013 Pearson Education, Inc.Magnetic Forces on Current-Carrying WiresA current perpendicular to the fieldexperiences a force in the directionof the right-hand rule.If a wire of length l contains acurrent I q/ t, it means a chargeq must move along its length in atime t l/v.Thus we have Il qv.Since q , the magneticforce on a current-carrying wire is: 2013 Pearson Education, Inc.Slide 32-140QuickCheck 32.19The horizontal wire can be levitated – held up againstthe force of gravity – if the current in the wire isA. Right to left.B. Left to right.C. It can’t be done withthis magnetic field. 2013 Pearson Education, Inc.Slide 32-14147
4/7/2016QuickCheck 32.19The horizontal wire can be levitated – held up againstthe force of gravity – if the current in the wire isA. Right to left.B. Left to right.C. It can’t be done withthis magnetic field. 2013 Pearson Education, Inc.Slide 32-142Example 32.13 Magnetic Levitation 2013 Pearson Education, Inc.Slide 32-143Example 32.13 Magnetic Levitation 2013 Pearson Education, Inc.Slide 32-14448
4/7/2016Example 32.13 Magnetic Levitation 2013 Pearson Education, Inc.Slide 32-145Example 32.13 Magnetic Levitation 2013 Pearson Education, Inc.Slide 32-146Magnetic Forces Between Parallel CurrentCarrying Wires: Current in Same Direction 2013 Pearson Education, Inc.Slide 32-14749
4/7/2016Magnetic Forces Between Parallel CurrentCarrying Wires: Current in Opposite Directions 2013 Pearson Education, Inc.Slide 32-148Forces on Current LoopsThe two figures show alternative but equivalent ways toview magnetic forces between two current loops.Parallel currents attract,opposite currents repel. 2013 Pearson Education, Inc.Opposite poles attract,like poles repel.Slide 32-149A Uniform Magnetic Field Exerts a Torque on aSquare Current Loopfront andback areopposite to each otherand cancel.Both top and bottomexert
If the north pole of one magnet is brought near the north pole of another magnet, they repel each other. Two south poles also repel each other, but the north pole of one magnet exerts an attractive force on the south pole of another magnet. Slide 32-20 Discovering Magnetism: Experiment 2
Introduction of Chemical Reaction Engineering Introduction about Chemical Engineering 0:31:15 0:31:09. Lecture 14 Lecture 15 Lecture 16 Lecture 17 Lecture 18 Lecture 19 Lecture 20 Lecture 21 Lecture 22 Lecture 23 Lecture 24 Lecture 25 Lecture 26 Lecture 27 Lecture 28 Lecture
Part One: Heir of Ash Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 Chapter 12 Chapter 13 Chapter 14 Chapter 15 Chapter 16 Chapter 17 Chapter 18 Chapter 19 Chapter 20 Chapter 21 Chapter 22 Chapter 23 Chapter 24 Chapter 25 Chapter 26 Chapter 27 Chapter 28 Chapter 29 Chapter 30 .
TO KILL A MOCKINGBIRD. Contents Dedication Epigraph Part One Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 Part Two Chapter 12 Chapter 13 Chapter 14 Chapter 15 Chapter 16 Chapter 17 Chapter 18. Chapter 19 Chapter 20 Chapter 21 Chapter 22 Chapter 23 Chapter 24 Chapter 25 Chapter 26
Physics 20 General College Physics (PHYS 104). Camosun College Physics 20 General Elementary Physics (PHYS 20). Medicine Hat College Physics 20 Physics (ASP 114). NAIT Physics 20 Radiology (Z-HO9 A408). Red River College Physics 20 Physics (PHYS 184). Saskatchewan Polytechnic (SIAST) Physics 20 Physics (PHYS 184). Physics (PHYS 182).
DEDICATION PART ONE Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 PART TWO Chapter 12 Chapter 13 Chapter 14 Chapter 15 Chapter 16 Chapter 17 Chapter 18 Chapter 19 Chapter 20 Chapter 21 Chapter 22 Chapter 23 .
Lecture 1: A Beginner's Guide Lecture 2: Introduction to Programming Lecture 3: Introduction to C, structure of C programming Lecture 4: Elements of C Lecture 5: Variables, Statements, Expressions Lecture 6: Input-Output in C Lecture 7: Formatted Input-Output Lecture 8: Operators Lecture 9: Operators continued
Advanced Placement Physics 1 and Physics 2 are offered at Fredericton High School in a unique configuration over three 90 h courses. (Previously Physics 111, Physics 121 and AP Physics B 120; will now be called Physics 111, Physics 121 and AP Physics 2 120). The content for AP Physics 1 is divided
Lecture 1: Introduction and Orientation. Lecture 2: Overview of Electronic Materials . Lecture 3: Free electron Fermi gas . Lecture 4: Energy bands . Lecture 5: Carrier Concentration in Semiconductors . Lecture 6: Shallow dopants and Deep -level traps . Lecture 7: Silicon Materials . Lecture 8: Oxidation. Lecture
