Sources-of-Magnetic-Field.ppt

Click to edit Master title style,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,Copyright 2012 Pearson Education Inc.Amended Scott Hildreth Chabot College 2016,PowerPoint,Lectures for,University Physics,Thirteenth Edition,Hugh D.Young and Roger A.Freedman,Lectures by Wayne Anderson,Click to edit Master title style,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,Click to edit Master title style,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,2016 Pearson Education Inc.,PowerPoint,Lectures for,University Physics,14th Edition,Hugh D.Young and Roger A.Freedman,Lectures by Jason Harlow,Click to edit Master title style,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,2016 Pearson Education Inc.,Click to edit Master title style,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,2016 Pearson Education Inc.,Click to edit Master title style,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,2016 Pearson Education Inc.,Click to edit Master title style,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,2016 Pearson Education Inc.,Chapter 28,Sources of Magnetic Field,Goals for Chapter 28,To determine the magnetic field produced by a moving charge,To study the magnetic field of an element of a current-carrying conductor,To calculate the magnetic field of a long,straight,current-carrying conductor,Goals for Chapter 28,To study the magnetic force between current-carrying wires,To determine the magnetic field of a circular loop,To use,Amperes Law,to calculate magnetic fields,Introduction,What can we say about the magnetic field due to a solenoid?,What actually creates magnetic fields?,We will introduce Amperes law to calculate magnetic fields.,Check out,CERN.The Large Hadron Collider(LHC).2008.YouTube.Accessed 10/29/12 from CERNTV.The Large Hadron Collider.2008.YouTube.Accessed 10/19/12 from,Euronews.Large Hadron Collider:A racetrack for particles.(2011)YouTube.Accessed 10/28/12 from,The magnetic field acts ON a moving charge,A moving charge IN a magnetic field experiences a force,So by Newtons 3,rd,law.,The moving charge must create a force on the source of the magnetic field!,How do you do that?,v,Source of Magnetic Field,-q,B Field,Force,The magnetic field of a moving charge,A moving charge generates a magnetic field at some point in space around it.,Charge q,moving with speed v in a direction,Point P in space some distance away,q,v,The magnetic field of a moving charge,The field direction,at that point,depends upon the directions of the velocity vector AND the relative location of the point in space.,Charge q,moving with speed v in a direction,Point P in space some distance away,q,v,B(r),r,The magnetic field of a moving charge,A moving charge generates a magnetic field that depends on the velocity of the charge.,The magnetic field of a moving charge,A moving charge generates a magnetic field that depends on the velocity of the charge.,B=(,m,0,/4,p),q(,v,x,r),/r,3,=,(,m,0,/4,p),q(,v,x,r),r,2,Magnetic force between moving protons,What is,m,0,?,m,0,e,0,=1/c,2,Magnitude,=,m,0,=4,p,x 10,-7,Units,=Tesla-meters/Amp(,T-m/A),or Webers/Amp-meter,(Wb/A-m),Ex 28.1 Magnetic force between moving protons,E field exists,(moving or not!),B Field of one,moving,particle creates FORCE on another,moving,particle,r,a,b,v,a,v,b,B,b at a,Force on UPPER proton?,E field direction?(+y),F,(E field),=q,2,/4,pe,0,r,2,F,(B field),=q,v,x,B,(from lower particle),B field direction?(+z),B,=(,m,0,/4,p),q(v,i,x,j),/r,2,F,B,=(,m,0,/4,p),q,2,v,2,/r,2,F,direction?(+y),Magnetic field of a current element,The total magnetic field of several moving charges is the vector sum of each field.,So a current of moving charges creates a B field!,Magnetic field of a current element,The total magnetic field of several moving charges is the vector sum of each field.,So a current of moving charges creates a B field!,Magnetic field of a current element,The total magnetic field of,several,moving charges is the vector sum of each field.,The,law of Biot and Savart,dB=(,m,0,/4,p),I(,dl,x,r),/r,2,Biot&Savart,Jean Baptiste Biot,Felix Savart,Magnetic field of a current element,The total magnetic field of several moving charges is the vector sum of each field.,Videos abound,!,Even more!,The,law of Biot and Savart,dB=(,m,0,/4,p),I(,dl,x,r),/r,2,Magnetic field of a straight current-carrying conductor,Law of Biot&Savart to a long straight conductor:,B=,0,I,/2,x,.,Magnetic field of a current segment,What is,B,field generated by 125 Amp current from 1.0 cm segment of wire 1.2 meters away(in+y)at P1?At P2(in the x-z plane)?,Magnetic field of a current segment,What is B field of 125 Amp current from 1.0 cm segment of wire 1.2 meters away at two points?,For P,1,:B=,m,0,/4,p,Idl/r,2,(-z direction),For P,2,B=,m,0,/4,p,I dl sin(30)/r,2,(also-z direction),For P,1,:B=,-8.7,x,10,-8,T(,z,),For P,2,:B=,-4.3,x,10,-8,T(,z,),Magnetic fields of long wires,Find,B,at,P,1,P,2,and,P,3,.,Magnetic fields of long wires,P,1,:-,m,0,I/2,p(2,d)+,m,0,I/2,p,(4d)=-,m,0,I/8,p,d,P,2,:+,m,0,I/2,p(,d)+,m,0,I/2,p,(d)=+,m,0,I/,p,d,P,3,:+,m,0,I/2,p(3,d)-,m,0,I/2,p,(d)=-,m,0,I/3,p,d,Forces between parallel wires,What force does each wire exert on the other?,Force/Length=,m,0,I,I,/2,p,r,Force/Length=1.0 x 10,4,N/m,Magnetic field of a circular current loop,Use Biot-Savart Law to find field a distance x away on axis from a coil with current I.,Remember VECTORS!,dB=(,m,0,/4,p),I(,dl,x,r),/r,3,y,z,x,a,r,P,x,Magnetic field of a coil,Direction of field using right-hand rule.,Magnetic field of a circular current loop,The Biot Savart law gives,B,x,=,0,Ia,2,/2(,x,2,+,a,2,),3/2,on the axis of the loop.,Magnetic field of a circular current loop,At,center,of,N,loops,where x=0,the field on the axis is,B,x,=,0,NI/,2,a,.,Graph B field vs.x,What about LOTS of coils?,A solenoid,Field of a solenoid,A,solenoid,consists of a helical winding of wire on a cylinder.,Field depends on#of turns per meter(“n”)and current I,2016 Pearson Education Inc.,Field of a toroidal solenoid,A,toroidal solenoid,is a,doughnut-shaped solenoid.,Magnetic fields for MRI,MRI(magnetic resonance imaging)requires magnetic field of 1.5 T.,Currents required are very high,so coils are bathed in liquid helium at a temperature of 4.2 K to keep from overheating.,2016 Pearson Education Inc.,Amperes law(general statement),Valid for conductors&paths of any shape.,If integral around closed path is zero,does,not,necessarily mean that B field is zero everywhere,only that total current through an area bounded by path is zero.,2016 Pearson Education Inc.,Amperes law(special case),Amperes,law,relates electric current to,line integral,around a closed path.,Special case of circular closed path centered on long,straight conductor carrying current,I,.,In this case integral is simple:,2016 Pearson Education Inc.,Amperes law(special case),Amperes law for a circular path around a long straight conductor.,Amperes law(general statement),Suppose several long,straight conductors pass through surface bounded by closed loop path.,The line integral of total magnetic field is proportional to,algebraic,sum,of currents.,2016 Pearson Education Inc.,Amperes law(general statement),Replace,I,in Amperes Law with,I,encl,=algebraic sum of currents enclosed or linked by integration path,Evaluate by using right-hand sign rule.,2016 Pearson Education Inc.,Field of a long cylindrical conductor,Cylindrical conductor with radius,R,carries current,I,.,Current is uniformly distributed over cross-sectional area of conductor.,2016 Pearson Education Inc.,Field of a long cylindrical conductor,A cylindrical conductor with radius,R,carries a current,I,.,To find the magnetic field,we apply Amperes law and find:,2016 Pearson Education Inc.,Magnetic fields of long conductors,Field of a solenoid,A,solenoid,consists of a helical winding of wire on a cylinder.,Field depends on#of turns per meter(“n”)and current I,2016 Pearson Education Inc.,The Bohr magneton,An electron moving with speed,v,in a circular orbit of radius,r,has an angular momentum and an oppositely directed orbital magnetic dipole moment,.,It also has a spin angular momentum and an oppositely directed spin magnetic dipole moment.,2016 Pearson Education Inc.,The Bohr magneton,As an electron orbits the nucleus of an atom,its magnetic dipole moment has a magnitude proportional to its orbital angular momentum.,Atomic angular momentum is,quantized,;its component in a particular direction is always an integer multiple of,h,/2,where,h,=6.626 10,34,Js is Plancks constant.,This means there is a fundamental unit of magnetic dipole moment,which is called the,Bohr,magneton,B,=,eh,/4,m,=9.274 10,24,J/T.,Electron spin also leads to a magnetic moment,which is about equal to one Bohr magneton.,2016 Pearson Education Inc.,Paramagnetism and diamagnetism,When an external magnetic field permeates a,paramagnetic,material,the result is that the magnetic field at any point is,greater,by a dimensionless factor,K,m,called the relative permeability of the material,than it would be if the material were replaced by vacuum.,If an external magnetic field permeates a,diamagnetic,material,the result is a magnetic field that is slightly,less,than it would be if the material were replaced by vacuum.,The amount by which the relative permeability differs from unity is called the magnetic susceptibility,denoted by,m,:,m,=,K,m,1,2016 Pearson Education Inc.,Magnetic susceptibilities of certain materials,2016 Pearson Education Inc.,Material,m,(,10,5,),Iron ammonium alum,66,Aluminum,2.2,Oxygen gas,0.19,Bismuth,16.6,Silver,2.6,Carbon(diamond),2.1,Copper,1.0,Paramagnetic,Diamagnetic,Ferromagnetism,In,ferromagnetic,materials,(such as iron),atomic magnetic moments tend to line up parallel to each other in regions called magnetic domains.,When there is no externally applied field,the domain magnetizations are randomly oriented.,When an external magnetic field is present,the domain boundaries shift;the domains that are magnetized in the field direction grow,and those that are magnetized in other directions shrink.,2016 Pearson Education Inc.,The Bohr magneton and paramagnetism,Table 28.1 shows the magnetic susceptibilities of some materials.,Diamagnetism and ferromagnetism,Follow the text discussion of,diamagnetism,and,ferromagnetism,.,Figure 28.27 at the right shows how,magnetic domains,react to an applied magnetic field.,Figure 28.28 below shows a magnetization curve for a ferromagnetic material.,Hysteresis,Applications of Electromagnetism in the News,New battery technology,Summer,Lauren(2013,November 1),Silicon Valley in Race for Battery Breakthrough,KQED Science,.,Understanding Earths Magnetic Field,Redd,N.(2013,October 9),Weird Shift of Earths Magnetic Field Explained.,S.,