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Physics 2102 Lecture 14

Physics 2102 Jonathan Dowling. Physics 2102 Lecture 14. Aurora Borealis. Ch28: Magnetic Forces on Current Wires. Star Quake on a Magnetar!. “I’ll be back…. Crossed Fields E vs. B. q. y. B. E. v. L. F E =qE. F E =ma  =>   y=qEL 2 /(2mv 2 ). F B =vqBF E.

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Physics 2102 Lecture 14

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  1. Physics 2102 Jonathan Dowling Physics 2102 Lecture 14 Aurora Borealis Ch28: Magnetic Forces on Current Wires Star Quake on a Magnetar! “I’ll be back….

  2. Crossed Fields E vs. B q y B E v L FE=qE FE=ma  =>  y=qEL2/(2mv2) FB=vqBFE FB=FE  => y=0  => v=E/B

  3. L Magnetic force on a wire. Note: If wire is not straight, compute force on differential elements and integrate:

  4. L R R L Example Wire with current i. Magnetic field out of page. What is net force on wire? By symmetry, F2will only have a vertical component, Notice that the force is the same as that for a straight wire, and this would be true no matter what the shape of the central segment!.

  5. L B I Example 4: The Rail Gun rails • 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? 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!

  6. Torque on a Current Loop: Principle behind electric motors. Rectangular coil: A=ab, current = i Net force on current loop = 0 But: Net torque is NOT zero! • For a coil with N turns, •  = N I A B sinq, where A is the area of coil

  7. Right hand rule: curl fingers in direction of current; thumb points along m Define: magnetic dipole moment m Magnetic Dipole Moment We just showed: t = NiABsinq N = number of turns in coil A=area of coil. As in the case of electric dipoles, magnetic dipoles tend to align with the magnetic field.

  8. +Q p=Qa -Q QE q QE Electric vs. Magnetic Dipoles

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