Physics 2102 Aurora Borealis Jonathan Dowling Lecture 19 MON 02 MAR Magnetic fields Ch 28 6 7 I ll be back Second Exam Review 6 7PM WED 04 MAR Nicholson 130 Second Exam Chapters 24 28 6 7PM THU 05 MAR Lockett 6 Circular Motion v F r Since magnetic force is perpendicular to motion the movement of charges is circular 2 v 2 out Fcentrifugal ma mr m r in magnetic F qvB FB FC mv 2 qv B r B into blackboard mv Solve r qB In general path is a helix component of v parallel to field is unchanged C v F B mv r qB Radius of Circlcular Orbit v qB r m Angular Frequency Independent of v electron r 2 r 2 mv 2 m T v qBv qB Period of Orbit Independent of v 1 qB f T 2 m Orbital Frequency Independent of v 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 d None of the above mv r qB Same charge q speed v and same 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 Don t know m or q separately Examples of Circular 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 F q vd B iL F q B iL B q F iL B Note If wire is not straight compute force on differential elements and integrate 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 Force on projectile F iLB Acceleration a F m iLB m v at iLBt m rails B L I projectile from F iL x B from F ma 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 Electromagnetic Slingshot These Devices Can Launch 1000kg Projectiles At Mach 100 at a Rate of 1000 Projectiles Per Second Using KE 1 2mv2 This corresponds to an output about 1012 Watts TeraWatt Uses Put Supplies on Mars Destroy NYC in about 10 minutes
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