MagnetismPHY232 – Spring 2007Jon Pumplinhttp://www.pa.msu.edu/~pumplin/PHY232(Ppt courtesy of Remco Zegers)PHY232 - Pumplin - magnetism 2magnetismMagnetic fields are produced by moving electrical charges – i.e., currents) macroscopic (e.g. currents in a wire) microscopic (electrons in atomic orbit and rotating around their own axis)PHY232 - Pumplin - magnetism 3magnets the magnetic field produced by electrons tend to cancel each other, so most materials are not magnetic in certain ‘ferromagnetic’ materials (iron) neighboring electrons can couple and form domains (< 1mm) that are magnetic. Since there are many domains that have different orientation, the material is overall not magnetized when an external magnetic field is applied the fields in the different domains align and the whole object becomes magnetic after the external field is removed, a material like iron becomes unmagnetized quickly, but some remain magnetized and can be used as ‘permanent’ magnets.PHY232 - Pumplin - magnetism 4para and ferro magnetsdo not retainany magnetismin absence of external fieldretains domainsin which magneticfield remain in the absence of external fieldsstrawberry in a B-fieldPHY232 - Pumplin - magnetism 5magnetic poles and fields magnets have ‘north’ and ‘south’ poles and field lines point in the direction of force on a North magnetic pole. unlike the case of electrical fields, where positive charges can exists separate from negative charges, north and south poles always come together. There are no monopoles discovered so far.demo:magnetic field lines (ohp)broken magnetPHY232 - Pumplin - magnetism 6One big magnet!Note that the geographical North pole is in fact the magnetic south pole B=0.3-0.6 x 10-4 TeslaWhy is it higher here?demo:compass needlescompassPHY232 - Pumplin - magnetism 7questionIf you are standing exactly at the (magnetic) south Pole (I.e. near the geographical north pole), and are holding a compass parallel with the earth’s surface, in which direction would the needle point?a) It would point roughly to the geographical southb) It could point anywherec) It would rotate with constant angular speedThe compass needle in fact wants to point into the earth(along the direction of the field line). But if hold parallel to earth, it can’t do that and will point wherever. There is no reason for it to rotate though.PHY232 - Pumplin - magnetism 8charged particles moving in a magnetic field A charged particle q that is moving with a velocity v in a magnetic field B will feel a force where q: charge of particlev: velocity of paticleB: magnetic field θθθθ: angle between velocity vector and field directionPHY232 - Pumplin - magnetism 9direction of force on charged paricles in B-field magnitude of the force you can find the direction of the force using the right hand rule. It holds for positive charges. For negative charges switch the direction of the forceIn the 3pm lecture (Section 2), we will use the versionof Right Hand Rules given in the Textbook.demo: bending the beam IPHY232 - Pumplin - magnetism 10example: electron in magnetic field an electron with v=1x106m/s is entering a area with B=1 T. The field is directed into the screen.a) in which direction will the electron be bent, if at all?b) how large is the force? what is the acceleration?x x x xx x x xx x x xa) use right hand rule:thumb is velocity (initially to the right)index finger is field (in the screen)middle finger is force perpendicular to bothswitch direction because negative chargeb) F=|q|vBsinθθθθ=1.6x10-19x 1x106x 1=1.6x10-13Na=F/m=1.6x10-13 N/9.11x10-31kg =1.76x1017m/s2PHY232 - Pumplin - magnetism 11question A Magnesium ion (Z=12) with all its electrons removed is moving in a field of 0.1 T as shown. What direction will the force act?a) into the screenb) out of the screenc) parallel to the B field lines and the screend) perpendicular to the B field lines and parallel to the screene) in the direction of motionMgv45oPHY232 - Pumplin - magnetism 12Charged particle in a magnetic field Let’s assume a charged particle is moving in a uniform magnetic field so that the velocity is perpendicular to the field. The particle will follow a curved pathand is directed towards the center Use Newton’s second law and theequation for centripetal accelerationdemo: bending the beam IIPHY232 - Pumplin - magnetism 13Magnetic spectrometersBeam fromcyclotronstarget chamberS800 spectrometerAt the cyclotronBending angle ~ 150oPHY232 - Pumplin - magnetism 14questionIn a nuclear reaction two types of fully ionized particles are created.120Sn with Z=50 and v=12.8814x107m/s (Tin)120Sb with Z=51 and v=13.099x107m/s (Antimony)Both have a mass of 1.991x10-25kg and pass through a 180omagnetic spectrometer with B=1T. If the detector used to locate the particles can separate events that are 2 mm away from each other, are 120Sn and 120Sb separated?r= mv/qBFor 120Sn: M=1.991x10-25kg v=12.8814x107m/sB=1T q=50x1.6x10-19C.RSn=3.2060 mFor 120Snb: M=1.991x10-25kg v=13.0990x107m/sB=1T q=51x1.6x10-19C.RSb=3.1961 mRSn-RSb=3.206-3.1961=9.9x10-3m = 9.9 mm thus separatedPHY232 - Pumplin - magnetism 15What we did so far Moving charged particles make magnetic field North and South poles cannot exist independently The magnitude of a force on a charge particle in a magnetic field: F=qvBsinθθθθ where θθθθ is the angle between v and B. The direction of the force is given by the (first) right-hand rule for + particles: use directly for – particles: after using the right hand-rule, reverse the direction of the force For a particle moving in a direction perpendicular to a magnetic fieldPHY232 - Pumplin - magnetism 16Question a proton is moving from left to right into a field of which the field lines point into the screen. As a result, the proton willa) continue along its original trajectoryb) bend upwardsc) bend downwardsd) bend into the screene) bend out of the screenx x x xx x x xx x x xprotonPHY232 - Pumplin - magnetism 17magnetic force on a conducting wire consider positive charges moving through a wire. Each particle feels a force, hence there is a net force on the wire N: total number of charges n: charges per unit volume Use: see earlier To get More general:  where θθθθ: angle between I and B vectorsIIPHY232 -