Physics 2102 Lecture 14PowerPoint PresentationSlide 3Slide 4Example 4: The Rail GunSlide 6Magnetic Dipole MomentElectric vs. Magnetic DipolesPhysics 2102 Physics 2102 Lecture 14Lecture 14Ch28: Magnetic Forces on Current WiresCh28: Magnetic Forces on Current WiresPhysics 2102Jonathan DowlingStar Quake on aMagnetar!“I’ll be back….Aurora BorealisCrossed Fields E vs. BCrossed Fields E vs. BFE=qEBEyqFB=vqBFEvLFE=ma=>y=qEL2/(2mv2)FB=FE=>y=0=>v=E/BMagnetic force on a wire.Magnetic force on a wire.dvLitiq ==LBvqFdrrr×=BLiBqLiqFrrrrr×=×=BLiFrrr×=BLdiFdrrr×=Note: If wire is not straight,compute force on differential elements and integrate:ExampleExampleiLBFF ==31θiBRdiBdLdF ==By symmetry, F2will only have a vertical component,iBRdiBRdFF 2)sin()sin(002∫∫===ππθθθ)(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?BIL• Force on projectile: F=ILB (from F=iLxB)• 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!projectilerailsTorque on a Current Loop:Principle behind electric motors.Net force on current loop = 0iaBFF ==31)sin(1θFF =⊥)sin(θτ iabBbFTorque ===⊥For a coil with N turns,=N IABsin, where A is the area of coilRectangular coil: A=ab, current =iBut: Net torque is NOT zero!nNiAˆ)(=μrnˆ,μrMagnetic Dipole MomentMagnetic Dipole MomentN=number of turns in coilA=area of coil.We just showed: =NiABsinRight hand rule:curl fingers in direction of current; thumb points along Define: magnetic dipole moment Brrr×=μτAs in the case of electric dipoles, magnetic dipoles tend to align with the magnetic field.Electric vs. Magnetic DipolesElectric vs. Magnetic
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