Physics 2102 Aurora Borealis Jonathan Dowling Physics 2102 Lecture 15 Magnetic fields Star Quake on a I ll be back Magnetar Use of Magnetic Fields in Your Everyday Life Magnetic Fields Electric fields are created microscopically by electric charges fields of elementary particles electrons protons macroscopically by adding the field of many elementary charges of the same sign Magnetic fields are created microscopically by magnetic moments of elementary particles electrons protons neutrons macroscopically by adding many microscopic magnetic moments magnetic materials or by electric charges that move electric currents Magnetic vs Electric Forces We know that an electric fields exists because it accelerates electric charges with a force independent of the velocity of the charge proportional to the electric charge FE qE We know that a magnetic field exists because it accelerates electric charges in a direction perpendicular to the velocity of the charge with a magnitude proportional to the velocity of the charge and to the magnitude of the charge FB q v x B Magnetic forces are perpendicular to both the velocity of charges and to the magnetic field electric forces are parallel to the field Since magnetic forces are perpendicular to the velocity they do no work W F r Speed of particles moving in a magnetic field remains constant in magnitude the direction changes Kinetic energy is constant no work Circular Motion v F r Since magnetic force is transverse to motion the natural movement of charges is circular v2 F ma m for circular motion r mv 2 Therefore q v B r mv r qB B into blackboard In general path is a helix component of v parallel to field is unchanged Example Two charged ions A and B traveling with a constant velocity v enter a box in which there is a uniform magnetic field directed out of the page The subsequent paths are as shown What can you conclude A v B v a Both ions are negatively charged b Ion A has a larger mass than B c Ion A has a larger charge than B mv r qB d None of the above Same speed and B for both masses So ion with larger mass charge ratio m q moves in circle of larger radius But that s all we know Cathode Ray Tube Old TVs Computer Monitors Hot cathode emits electrons Get accelerated by positive plate Might be deflected using plates Produce point of light on screen In a magnetic field B r r v B v Fe Dot shifts sideways Examples of Motion in Magnetic Fields Aurora borealis northern lights Synchrotron Suppose you wish to accelerate charged particles as fast as you can Linear accelerator long Fermilab Batavia IL 1km Magnetic force on a wire L L q it i vd r r r F q vd B r r iL r r r F q B iL B q r r r F iL B Note If wire is not straight compute force on differential elements and integrate r r r dF i dL B Example Wire with current i Magnetic field out of page What is net force on wire F1 F3 iLB dF iBdL iBRd By symmetry F2 will only have a vertical component 0 0 F2 sin dF iBR sin d 2iBR Ftotal F1 F2 F3 iLB 2iRB iLB 2iB L R Notice that the force is the same as that for a straight wire and this would be true no matter what the shape of L R R L the central segment Example 4 The Rail Gun Conducting projectile of length 2cm mass 10g carries constant current 100A between two rails Magnetic field B 100T points outward Assuming the projectile starts from rest at t 0 what is its speed after a time t 1s rails B L I projectile Force on projectile F ILB from F iL x B Acceleration a iLB m from F ma v t iLBt m from v v0 at 100A 0 02m 100T 1s 0 01kg 2000m s 4 473mph MACH 8 Rail guns in the Eraser movie Rail guns are hyper velocity weapons that shoot aluminum or clay rounds at just below the speed of light In our film we ve taken existing stealth technology one step further and given them an X ray scope sighting system notes director Russell These guns represent a whole new technology in weaponry that is still in its infancy though a large scale version exists in limited numbers on battleships and tanks They have incredible range They can pierce three foot thick cement walls and then knock a canary off a tin can with absolute accuracy In our film one contractor has finally developed an assault sized rail gun We researched this quite a bit and the technology is really just around the corner which is one of the exciting parts of the story Warner Bros production notes 1996 http movies warnerbros com eraser cmp prodnotes html tech Also INSULTINGLY STUPID MOVIE PHYSICS http www intuitor com moviephysics Principle behind electric motors Torque on a Current Loop Rectangular coil A ab current i Net force on current loop 0 But Net torque is NOT zero F1 F3 iaB F F1 sin Torque F b iabB sin For a coil with N turns N I A B sin where A is the area of coil Magnetic Dipole Moment We just showed NiABsin N number of turns in coil A area of coil Define magnetic dipole moment r NiA n r n Right hand rule curl fingers in direction of current thumb points along r r r B As in the case of electric dipoles magnetic dipoles tend to align with the magnetic field Electric vs Magnetic Dipoles r NiA n Q p Qa Q QE QE r r r p E r r r B
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