Physics 2102 Aurora Borealis Jonathan Dowling Physics 2102 Lecture 14 Ch28 Magnetic Forces on Current Wires Star Quake on a I ll be back Magnetar Crossed Fields E vs B q v B E y L FE qE FB vqBFE FE ma y qEL2 2mv2 FB FE y 0 v E B Magnetic force on a wire L L q i t i vd r r r F q vd B r r iL r r r F q B i L B q r r r F i L 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 0 0 By symmetry F2 will only have a vertical component 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 from v v0 at v t iLBt m 100A 0 02m 100T 1s 0 01kg 2000m s 4 473mph MACH 8 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 iabBsin 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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