Lecture 8 Magnetic Fields Chp. 29• Cartoon Magnesia, Bar Magnet with N/S Poles, Right Hand Rule• Topics– Magnetism is likable, Compass and diclinometer, Permanent magnets– Magnetic field lines, Force on a moving charge, Right hand rule,– Non-uniform magnetic field– Force on a current carrying wire, Torque on a current loop• Demos– Globe– Natural magnetic rock– Compass and diclinometer– Iron fillings and bar magnets– Compass needle array– Pair of gray magnets– CRT illustrating electron beam bent bent by a bar magnet– Gimbal mounted bar magnet– Wire jumping out of a horsehoe magnet.– Coil in a magnetMagnetic Fields• Magnetism has been around as long as there has been an Earth withan iron magnetic core.• Thousands of years ago the Chinese built compasses for navigation inthe shape of a spoon with rounded bottoms on which they balanced(Rather curious shape for people who eat with chopsticks).• Certain natural rocks are ferromagnetic – having been magnetized bycooling of the Earth’s core.• Show a sample of natural magnetic rock. Put it next to manycompasses.Magnetism’s Sociabilities• Magnetism has always has something of a mystic aura about it. It isusually spoken of in a favorable light.• Animal magnetism, magnetic personality, and now you can wearmagnetic collars, bracelets, magnetic beds all designed to make youhealthier – even grow hair.• We do not have the same feeling about electricity. If you live nearelectric power lines, the first thing you want to do is to sue the electriccompany.Compass and Declinometer• In 1600 William Gilbert used a compass needle to show how it orienteditself in the direction of the north geographic pole of the Earth, whichhappens to be the south magnetic pole of the Earth’s permanentmagnetic field.• Show compass and declinometer. Each has a slightly magnetizedneedle that is free to rotate. The compass lines up with the componentof the magnetic field line parallel to the surface of the Earth. Thedeclinometer lines up with the actual magnetic field line itself. It saysthat the angle between the field lines and the surface is 71 degrees asmeasured from the south.• Show model of Earth field lines assuming a uniformly magnetizedsphere• Basically there are two types of magnets: permanent magnets andelectromagnets• Show field lines for a bar magnet. Show bar magnet surroundedby compass needle array.Permanent Magnets• Bar magnet is a model of a ferromagnetic material that can bepermanently magnetized. Other ferromagnetic materials arecobalt and nickel.• The origin of magnetism in materials is due mostly to the spinningmotion of the charged electron on its own axis. There is a smallcontribution from the orbital motion of the electron.+avElectronorbitingnucleusMagnetic dipoleMagneticdipolesElectronspinning onits axise-Atomic origin of magnetic fieldPermanent Magnets (continued)• In ferromagnetic materials there are whole sections of the ironcalled domains where the magnetism does add up fromindividual electrons. Then there are other sections or domainswhere contributions from different domains can cancel. However,by putting the iron in a weak magnetic field you can align thedomains more or less permanently and produce a permanentbar magnet as you see here.• In nonmagnetic materials the contributions from all The electrons cancel out. Domains are not even formed.Magnetic field lines donot stop at surface.They are continuous.They make completeloops.Field lines for a barmagnet are the same asfor a current loopMagnetic field linesSimilarities to electric lines• A line drawn tangent to a field line is the direction of the field at thatpoint.• The density of field lines still represent the strength of the field.Differences• The magnetic field lines do not terminate on anything. They formcomplete loops. There is no magnetic charge on as there was electriccharge in the electric case. This means if you cut a bar magnet in halfyou get two smaller bar magnets ad infinitum all the way down to theatomic level – Magnetic atoms have an atomic dipole – not a monopoleas is the case for electric charge.• They are not necessarily perpendicular to the surface of theferromagnetic material.!!"==#"==#AdE flux Electric AdB flux Magnetic EB!!!!Definition of magnetic Field• definition of a magnetic field• The units of B are or in SI units(MKS).This is called a Tesla (T). One Tesla is a very strong field.• A commonly used smaller unit is the Gauss. 1 T = 104 G(Have to convert Gauss to Tesla in formulas in MKS)• In general the force depends on angle . This is calledthe Lorentz ForceqvFB =)(.smCN).( mANBvqF!!!!=In analogy with the electric force on a point charge, the correspondingequation for a force on a moving point charge in a magnetic field is:Magnitude of– Direction of F is given by the right hand rule (see next slide).• If ! = 90, then he force = and the particle moves in a circle.v B sin(0o) = 0 F = 0FBvBvqFm!!!!=EqFe!!=!sinqvBFm=qvBIf the angle between v and B is ! = 0, then the force = 0.• Consider a uniform B field for simplicity.B v!!Use right hand rule to find the direction of F+Positive ChargeRotate v into B through the smaller angle " and the force F will be in the directiona right handed screw will move.BvqFm!!!!=!Fm= q!v !!Bxyzijk ˆv = vxˆi + vyˆj!B = Bxˆi + Byˆj !F =ˆiˆjˆkvxvy0BxBy0!"###$%&&&=vy0By0!"#$%&ˆi +0 vx0 Bx!"#$%&ˆj +vxvyBxBy!"#$%&ˆk!F =ˆiˆjˆkvxvy0BxBy0!"###$%&&&= (vxBy' Bxvy)ˆkNote !F ! xy planeMotion of a point positive charge “ ” in a magnetic field.For a “+” charge, the particle rotates counter clockwise.For a “-” charge, the particle rotates counter clockwise.•Since F # v, the magnetic force does no work on the particle.W = F • d = 0 ; F # d•This means kinetic energy remains constant.•The magnitude of velocity doesn’t change.•Then the particle will move in a circle forever.•The B field provides the centripetal force needed for circular motion. = qvBsin90oDirection of the RHR (right hand rule)Magnitude of F = qvBB is directed into the paperrxx xxxxFvFvFv +BvF!!!!!BvqFm!!!!=Apply Newton’s 2nd Law to circular motionWhat is the period of revolution of the motion?qvBrmvmaF ===2qBmvr =Radius of the orbitImportant formula inPhysicsvarrva2= T =2!rv=2!mqB= period = TNote the period is independent of the radius, amplitude, and velocity. Example ofsimple harmonic motion in 2D.T is
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