Understanding Magnetic Fields and Circular Motion in Physics: Exam Review & Key Concepts

1. Physics 2102 Jonathan Dowling Lecture 14: TUE 09 MAR Aurora Borealis Magnetic Fields II Ch.28.6-10 “They are not supposed to exist….”

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

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

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

5. A B v v Example Two charged ions A and B traveling with a constant velocity venter 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) 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.

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

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

9. 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!.

10. 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 = F/m = iLB/m (from F = ma) • v = at = iLBt/m (from v = v0 + at) • = (100A)(0.02m)(100T)(1s)/(0.01kg) = 2000m/s • = 4,473mph = MACH 8!

11. 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/

12. Rail guns in Transformers II

13. Electromagnetic Slingshot These Devices Can Launch 1000kg Projectiles At Mach 100 at a Rate of 1000 Projectiles Per Second. Using KE = 1/2mv2 This corresponds to an output about 1012 Watts = TeraWatt. Uses: Put Supplies on Mars. Destroy NYC in about 10 minutes.

15. 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

16. 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.

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

18. L Magnetic Force on a Wire.

19. i . (28-12)

20. 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

21. 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.

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