Lecture 19: MON 02 MARPowerPoint PresentationSlide 3Slide 4ExampleExamples of Circular Motion in Magnetic FieldsSlide 7Slide 8Example 4: The Rail GunRail guns in the “Eraser” movieSlide 11Slide 12Lecture 19: MON 02 MAR Lecture 19: MON 02 MAR Magnetic fields Magnetic fields Ch.28.6-7 Physics 2102Jonathan Dowling“I’ll be back….Aurora BorealisQuickTime™ and a decompressorare needed to see this picture.Second Exam Review:6-7PM WED 04 MAR Nicholson 130Second Exam (Chapters 24–28):6–7PM THU 05 MAR Lockett 6Circular Motion:Since magnetic force is perpendicular to motion, the movement of charges is circular.B into blackboard.vF€ FB= FC→ qv B =mv2r€ FB= FC→ qv B =mv2rIn general, path is a helix (component of v parallel to field is unchanged).In general, path is a helix (component of v parallel to field is unchanged).r€ Fcentrifugalout= ma = mrω2= mv2r€ Fcentrifugalout= ma = mrω2= mv2r€ Fmagneticin= qvB€ Fmagneticin= qvB€ Solve : r =mvqB€ Solve : r =mvqB..electronrBvrFrCr€ r =mvqB€ r =mvqB€ ω =vr=qBm€ ω =vr=qBm€ T ≡2πrv=2πmvqBv=2πmqB€ T ≡2πrv=2πmvqBv=2πmqB€ f ≡1T=qB2πm€ f ≡1T=qB2πmRadius of Circlcular OrbitRadius of Circlcular OrbitAngular Frequency:Independent of v Angular Frequency:Independent of v Period of Orbit:Independent of v Period of Orbit:Independent of v Orbital Frequency:Independent of v Orbital Frequency:Independent of vExampleExampleTwo 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?qBmvr = 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. 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.(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.vvABAurora borealis(northern lights)SynchrotronLinear accelerator (long).Fermilab,Batavia, IL (1km)Suppose you wish to accelerate chargedparticles as fast as you can.Examples of Circular Motion Examples of Circular Motion in Magnetic Fieldsin Magnetic FieldsMagnetic Force on a Wire.Magnetic Force on a Wire.dvLitiq ==LBvqFdrrr×=BLiBqLiqFrrrrr×=×=BLiFrrr×=BLiFrrr×=BLdiFdrrr×=BLdiFdrrr×=Note: If wire is not straight,compute force on differential elements and integrate:ExampleExampleiLBFF ==31iLBFF ==31θiBRdiBdLdF ==θiBRdiBdLdF ==By symmetry, F2 will only have a vertical component,iBRdiBRdFF 2)sin()sin(002∫∫===ππθθθ)(22321totalRLiBiLBiRBiLBFFFF +=++=++=)(22321totalRLiBiLBiRBiLBFFFF +=++=++=Notice that the force is the same as that for a straight wire,L LR Rand this would be true nomatter what the shape of the central segment!.Wire with current i.Magnetic field out of page.What is net force on wire?Example 4: The Rail GunExample 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?•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?BIL• Force on projectile: F= iLB (from F = iL x B)• Acceleration: a = F/m = iLB/m (from F = ma)• v = at = iLBt/m (from v = v0 + at) =F(100A)(0.02m)(100T)(1s)/(0.01kg)F= 2000m/s=F4,473mphF= MACH 8!• Force on projectile: F= iLB (from F = iL x B)• Acceleration: a = F/m = iLB/m (from F = ma)• v = at = iLBt/m (from v = v0 + at) =F(100A)(0.02m)(100T)(1s)/(0.01kg)F= 2000m/s=F4,473mphF= MACH 8!projectilerailsRail 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 onbattleships 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#techAlso: INSULTINGLY STUPID MOVIE PHYSICS: http://www.intuitor.com/moviephysics/Electromagnetic SlingshotThese Devices CanLaunch 1000kg ProjectilesAt Mach 100 at a Rate of 1000 Projectiles Per Second.Using KEF=F1/2mv2This corresponds to an output about 1012 Watts = TeraWatt.Uses: Put Supplies on Mars. Destroy NYC in about 10 minutes.QuickTime™ and aH.264 decompressorare needed to see this
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