1 / 16

Lecture 20

Lecture 20. Applications. Magnetic force on a current. Charged particles in magnetic field. LHC dipole magnet. Circular motion in a uniform B field. uniform B v is initially perpendicular to B. → Uniform circular motion. F. B. proton. v. F. Helix.

bobby
Download Presentation

Lecture 20

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Lecture 20 Applications. Magnetic force on a current Charged particles in magnetic field LHC dipole magnet

  2. Circular motion in a uniform B field • uniform B • v is initially perpendicular to B → Uniform circular motion F B proton v

  3. F Helix If the initial velocity of the charges is NOT perfectly perpendicular to B…

  4. Charge q acquires its speed between two plates with potential difference V: Thompson’s q/m experiment Radius of circular trajectory of charge q in uniform field B: • With a known voltage and B-field, if we measure R we can predict q/m • In 1897, Thomson measured the q/m ratio for “cathode rays” (electrons emitted by a hot filament). • He found that all rays yield the same q/m ratio, for any material source. • Electrons are a fundamental constituent of all matter!

  5. Mass spectrometer Used to identify substances • Electrostatically accelerated electrons knock electron(s) off the atom  positive ion (q =|e|) • Accelerate the ion in a known potential difference V • Pass the ions through a known B field: Deflection depends on mass: lighter ions deflect more, heavier less • Electrically detect the ions which “made it through” • Change B (or V ) and try again

  6. Applications: • Chemical analysis • Carbon dating: “14C method” • Paleogeology: Determine relative abundances of isotopes (they decay at different rates geological age) • Space exploration: Determine what’s on the moon, Mars, etc. • Mars rover Curiosity

  7. Particle accelerators Magnetic fields cannot do work! Like the Large Hadron Collider (LHC) at CERN Huge magnets keep the particles moving in circles. In some sections, electric fields (NOT magnetic fields) accelerate the particles E B E

  8. negative particle positive particle B e+ e- B into screen Measuring the mass of a particle in an accelerator Measuring the curvature of a path is the usual way of measuring momentum of particles in high energy experiments.

  9. Discovering short-lived particles Use momentum and energy conservation to determine mass of “parent particle”: example Higgs boson → ZZ → 2(μ+μ−) 500x more data

  10. Charge in a section of length dl : Force on a section of length dl : Lecture 14: q v For a straight segment of length L DEMO: Magnet on wire Magnetic force on a current-carrying wire A current I flows in a wire with cross-section A. There are n carriers of charge q0 per unit volume.

  11. Example: Electromagnetic rail gun L v y x z A conducting bar (orange segment) of mass m can slide without friction on the horizontal wires that are connected to a source that provides a constant current I. There is a uniform magnetic field B into the screen. The bar is initially at rest. Find the velocity of the bar as a function of time. I I L

  12. This is still true!! L v y x z Wait a minute: Magnetic fields cannot do work! Where does this additional kinetic energy come from??? Answer in chapter 29 (lectures 25-26): We’ll see that keeping that current constant is not so obvious, even for ideal wires without resistance. When the bar moves, current tends to decrease (Lenz’s law). The extra energy comes from the additional potential energy that the battery needs to supply to keep the current the same. ie, an electric field is doing the work. I I L

  13. In-class example: Lifting bar L A voltage source and variable resistor are used to sweep current through a 1.0 m long rod with a mass of 100 g in a uniform, horizontal B field of 1000 G (0.1 T). The circuit is horizontal (shown from above here). If the rod is simply resting on two end supports, for what current will it lift off of the supports? I • 3.4 A • 9.8 A • 12.4 A • 18.6 A • 32.4 A V L And yes, the magnetic field is still not doing any work!

  14. Speakers B F I B F I Note: B field in speakers is radial

  15. F I Positive charges in the bar feel a force up CCW current is established in the closed circuit! I can light a bulb! More about this in lectures 25-26. Of course, this energy comes from your muscles and not from the magnetic field… Ultimate DIY: lighting a bulb with your hands U-shaped conducting wire + conducting bar I push at constant speed v in a uniform B field as shown (no battery!)

More Related