Review Physics 122 11/10/2018 Lecture XXIV

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 11/10/2018 Lecture XXIV

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 11/10/2018 Lecture XXIV

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 11/10/2018 Lecture XXIV

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 11/10/2018 Lecture XXIV

Gauss’s law Describes electric field created by electric charges 11/10/2018 Lecture XXIV

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 11/10/2018 Lecture XXIV

Application of Gauss’s law Infinitely long thick charged wire, radius R Charge per unit length Q/l=l r>R: r<R: 11/10/2018 Lecture XXIV

Amper’s law Describes magnetic field created by moving charges = currents 11/10/2018 Lecture XXIV

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 11/10/2018 Lecture XXIV

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 11/10/2018 Lecture XXIV

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 11/10/2018 Lecture XXIV

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 11/10/2018 Lecture XXIV

Motion in electric fields a is always || to net F Remember v is not always || to a (projectile, circular motion) - - - - vx vy + + + + vx=const vy=at=tF/m=tEq/m 11/10/2018 Lecture XXIV

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 11/10/2018 Lecture XXIV

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 11/10/2018 Lecture XXIV

Cyclotron frequency Frequency does not depend on v! For a given particle type (q,m=const) it depends only on B 11/10/2018 Lecture XXIV

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 + + + + - - - - + 11/10/2018 Lecture XXIV

Sources of E and B Sources of E Sources of B In vacuum Electric charges Changing magnetic field Sources of B Currents Changing electric field In vacuum No currents, no charges 11/10/2018 Lecture XXIV

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 11/10/2018 Lecture XXIV

EM wave 11/10/2018 Lecture XXIV

EM wave This is the speed of light!!! Light is an EM wave!!! 11/10/2018 Lecture XXIV

Energy in EM wave EM waves transport energy Energy density: 11/10/2018 Lecture XXIV

11/10/2018 Lecture XXIV