Physics 2113 Aurora Borealis Jonathan Dowling Lecture 27

Physics 2113 Aurora Borealis Jonathan Dowling Lecture 27: FRI 20 MAR Magnetic Fields III “They are not supposed to exist…. ”

Magnetic Force on a Wire. L

Magnetic Force on a Wire L Note: If wire is not straight, compute force on differential elements and integrate: i

i . (28 -12)

28. 8. 2. A portion of a loop of wire passes between the poles of a magnet as shown. We are viewing the circuit from above. When the switch is closed and a current passes through the circuit, what is the movement, if any, of the wire between the poles of the magnet? a) The wire moves toward the north pole of the magnet. b) The wire moves toward the south pole of the magnet. c) The wire moves upward (toward us). d) The wire moves downward (away from us into board). e) The wire doesn’t move. i

Example Wire with current i. Magnetic field out of page. What is net force on wire? By symmetry, F 2 will only have a vertical component, Notice that the force is the same as that for a straight wire of length R, and this would be true no matter what the shape of L R R L the central segment!.

i

SP 28 -06 ICPP: Find Direction of B i

Example 4: The Rail Gun • Conducting projectile of length 2 cm, mass 10 g carries constant current 100 A between two rails. • Magnetic field B = 100 T points outward. • Assuming the projectile starts from rest at t = 0, what is its speed after a time t = 1 s? • Force on projectile: F= i. LB • Acceleration: a = F/m = i. LB/m • v = at = i. LBt/m rails B I L projectile (from F = i. L x B) (from F = ma) (from v = v 0 + at) = (100 A)(0. 02 m)(100 T)(1 s)/(0. 01 kg) = 2000 m/s = 4, 473 mph = 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/

Rail guns in Transformers II

Rail guns in Reality!

Electromagnetic Slingshot These Devices Can Launch 1000 kg Projectiles At Mach 100 at a Rate of 1000 Projectiles Per Second. Using KE = 1/2 mv 2 This corresponds to an output about 1012 Watts = Tera. Watt. Uses: Put Supplies on Mars 80 days after launch. Current time to Mars on Ordinary Rocket? 1. 5 -3 years.

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! For a coil with N turns, τ = N I A B sinθ , where A is the area of coil

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

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

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

1 and 3 are “downhill”. 2 and 4 are “uphill”. U 1 = U 4 > U 2 = U 3 τ is biggest when B is at right angles to μ

ICPP