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Review

Review. Physics 122. Final Exam. Saturday, December 17, 8:30 am (sorry!) - Hoygt Final exam is based on the entire course PHY122. Last homework will be based on the entire course to give you more time to prepare for the final. 40% of the final grade. Grading. Workshops: 5%

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Review

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  1. Review Physics 122 Lecture XXIV

  2. Final Exam • Saturday, December 17, 8:30 am (sorry!) - Hoygt • Final exam is based on the entire course PHY122. • Last homework will be based on the entire course to give you more time to prepare for the final. • 40% of the final grade Lecture XXIV

  3. Grading • Workshops: 5% • Homework: 5% • Hour Exams: 40% • Final Exam: 40% • Laboratory: 10% • Total: 100% • 90% or above: A 88-89.9 – A- 85-87.9 – B+ • 80% - 85% : B 78-79.9 – B- 75-77.9 – C+ • 70% - 75%: C 68-69.9 – C- 65-67.9 – D+ • 60% - 65%: D • Under 60% : F Lecture XXIV

  4. Electricity and magnetism • The most important concept - electromagnetic field • First introduced for convenience • Electric charge changes the properties of space around them = creates electric field • Other charges feel this change  interaction between electric charges is mediated by the electric field • Change in electromagnetic field propagates with finite velocity (c ) = electromagnetic wave – proof that EM field is a reality Lecture XXIV

  5. Maxwell’s equations = constitution for EM field • Gauss’ law – field lines start on + and end on - • No magnetic charge – closed field lines • Changing magnetic flux acts like a source of electric field • Amper’s law with extra term Lecture XXIV

  6. Gauss’s law • Describes electric field created by electric charges Lecture XXIV

  7. Gauss Coulomb • Calculate E of point like (+) charge Q • Consider sphere radius r centered at the charge • Spherical symmetry: E is the same everywhere on the sphere, perpendicular to the sphere Lecture XXIV

  8. Application of Gauss’s law • Infinitely long thick charged wire, radius R • Charge per unit length Q/l=l • r>R: • r<R: Lecture XXIV

  9. Amper’s law • Describes magnetic field created by moving charges = currents Lecture XXIV

  10. Ampere’s Law • In a way similar to Gauss’s law for E and Q • Not flux, integral over closed path • Only component of B parallel to dl contributes to integral Lecture XXIV

  11. Application of Ampere’s Law • Thick wire of radius R carries current I. What is B(r ) in and outside of the wire? • Current through unit area: • Current through circle radius r<R • Path integral over radius r • Ampere’s law • For r>R – same as thin wire Lecture XXIV

  12. Forces on charges • Maxwell’s equations tell us about the EM field • They tell nothing about the force that this field exerts on charges – Lorentz force Lecture XXIV

  13. Crossed fields • Electric field changes kinetic energy of charged particle qDV=mv2/2 • Magnetic field does not change KE, only direction • Lorentz force: • Force due to E is parallel to E • Force due to B is perpendicular to B and to velocity of moving particle Lecture XXIV

  14. a is always || to net F Remember v is not always || to a (projectile, circular motion) Motion in electric fields - - - - vx vy + + + + vx=const vy=at=tF/m=tEq/m Lecture XXIV

  15. Magnetic force on moving charge • Magnetic force F is perpendicular to the velocity v of a particle with charge q F=qvB sin q • Magnetic field does not change the magnitude of particle’s velocity, only its direction. Charged particles move in circles in constant magnetic field Lecture XXIV

  16. Magnetic force on moving charge • Circular motion • Magnetic force = Centripetal force F=qvB • Centripetal acceleration a=v2/R • Newton’s second law F=ma qvB=mv2/R In experiments B is known, q=e most of the time, Measure R- measure mv For a given v measure m – magnetic spectrometer Lecture XXIV

  17. Cyclotron frequency Frequency does not depend on v! For a given particle type (q,m=const) it depends only on B Lecture XXIV

  18. Particle selector • Crossed E and B fields: • For one given velocity electric force exactly compensates magnetic force • Only particles with this value of velocity emerge from particle selector + + + + - - - - + Lecture XXIV

  19. Sources of E and B • Sources of E • Electric charges • Changing magnetic field • Sources of B • Currents • Changing electric field • In vacuum • No currents, no charges Lecture XXIV

  20. Radiation from an AC antenna • Changing electric field creates magnetic field • Changing magnetic field creates electric field • Change propagates with a finite velocity • Electromagnetic wave – proof of unification Lecture XXIV

  21. EM wave Lecture XXIV

  22. EM wave This is the speed of light!!! Light is an EM wave!!! Lecture XXIV

  23. Energy in EM wave • EM waves transport energy • Energy density: Lecture XXIV

  24. Lecture XXIV

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