Physics 2102 Aurora Borealis Jonathan Dowling Lecture 14

Physics 2102 Aurora Borealis Jonathan Dowling Lecture 14: TUE 09 MAR Magnetic Fields II Ch. 28. 6 -10 “They are not supposed to exist…. ”

Second Exam Review: 10: 40 AM– 12: 00 N THU 11 MAR Nicholson 109 in Class Second Exam (Chapters 24– 28): 6– 7 PM THU 11 MAR Lockett 6

Circular Motion: Since magnetic force is perpendicular to motion, the movement of charges is circular. v F r B into blackboard. In general, path is a helix (component of v parallel to field is unchanged).

. electron C . Radius of Circlcular Orbit r Angular Frequency: Independent of v Period of Orbit: Independent of v Orbital Frequency: Independent of v

Example Two 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? A v B v (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. 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.

Examples of Circular Motion in Magnetic Fields Aurora borealis (northern lights) Synchrotron Suppose you wish to accelerate charged particles as fast as you can. Linear accelerator (long). Fermilab, Batavia, IL (1 km)

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

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, 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 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? rails B L I projectile • Force on projectile: F= i. LB (from F = i. L x B) • Acceleration: a = F/m = i. LB/m (from F = ma) • v = at = i. LBt/m (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

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. Destroy NYC in about 10 minutes.

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, t = N I A B sinq, where A is the area of coil

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 m 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 Force on a Wire. L

i . (28 -12)

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, t = N I A B sinq, where A is the area of coil

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 m 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