1. PHYS 241 Final Exam Review Kevin Ralphs

2. Overview General Exam Strategies Concepts Practice Problems

3. General Exam Strategies Don’t panic!!! If you are stuck, move on to a different problem to build confidence and momentum “Play” around with the problem Take fifteen to twenty minutes before the exam to relax… no studying. Dimensional analysis is a good tool, but can give false results

4. Concepts EMF Faraday’s Law Inductance AC Circuits – RMS – Reactance – Impedance – Phasors Displacement Current Electromagnetic Waves (Light) – Wave/Particle Duality – Poynting Vector

5. Concepts Optics – Refraction Index of Refraction Snell’s Law – Total Internal Reflection – Malus’s Law – Mirrors – Lenses – Diffraction

6. Electromotive Force (EMF)

7. Why do I care? – If a particle is free to move around in space, this is not all that helpful, but when they are constrained to move on a specified path (like an electronic circuit), it becomes well-defined. Note: 1.This is not a force, it has units of volts 2.This is not a potential, the path taken matters very much

8. Motional EMF When a conductor moves through a magnetic field, it acquires an EMF (this is more along the lines of the two terminal definition) This happens because a Lorentz force from the magnetic field shuffles charges to opposite ends of the conductor This sets up a voltage like a parallel plate capacitor bringing the charges into an equilibrium

9. Motional EMF

10. Farraday’s Law

12. What does it tell me? – A changing magnetic field creates a non-conservative electric field – Anything that affects that flux integral induces an EMF in a loop Why should I care? – Without this law, you could not see, there would be no cell phones or radio: electromagnetic waves exist because of this – Inductors and transformers exploit this phenomenon

13. Lenz’s Law What does it tell me? – When the flux through a loop changes, a current is produced that fights this change Why should I care? – This principle is how you determine the direction of an induced current

14. Lenz’s Law If you are having problems with this, you are not alone – People spend thousands of hours researching this (no kidding) The idea is to find the direction of the induced magnetic field and use the right hand rule to find the current To find the direction of the induced field – Note the direction of the original field through the loop – Determine whether this field is getting stronger or weaker – The direction of the induced field will maintain the status quo

15. Inductance

16. Why should I care? – This is the sister component to the capacitor making it one of the most fundamental electronic components CapacitorInductor Depends on geometry and material between the plates Depends on geometry and material in intervening space Proportionality between charge and voltage Proportionality between flux and current Stores energy in an electric fieldStores energy in a magnetic field Causes current to lag voltageCauses current to lead voltage Current starts at maximum and drops to zero Current starts at zero and increases to maximum

17. Alternating Current (AC) - RMS

18. AC - Reactance

19. AC - Impedance What does it tell me? – It represents the relationship (magnitude and phase difference) between the applied voltage and the current Why should I care? – Impedance provides a compact way to carry a lot of information about your circuit

20. AC - Impedance

21. AC - Phasors A phasor is a graphical representation of the relationship between voltage and current in a system This exploits the power of complex numbers as both vectors and rotations The phasor rotates through the complex plane and the real projections of the phasor give the measured value See Demonstration

22. Displacement Current

23. Why do I care? – The correction completes Ampere’s law bringing it in agreement with the Biot-Savart Law – Like Faraday’s law, this allows for the propagation of electromagnetic waves

24. Poynting Vector Work done insideEnergy flowing outChange in internal energy

25. Poynting Vector

26. Index of Refraction

27. Snell’s Law

28. Malus’s Law

29. Assumptions/Conventions

30. Mirrors Rules for Ray Diagrams Parallel RaysReflected through focal point Focal RaysReflected parallel to optical axis Radial RaysReflected back on itself Sign Convention s is positive if object is on the incident-light side s’ is positive if the image is on the reflected-light side R is positive if the mirror is concave

31. Lenses Rules for Ray Diagrams Parallel RaysRefracted through focal point Focal RaysRefracted parallel to optical axis Central RaysNo deflection when refracted Sign Convention s is positive if object is on the incident-light side s’ is positive if the image is on the refracted-light side r is positive if center of curvature is on the refracted-light side

32. Diffraction What does it tell me? – How a wave behaves near objects – Only an appreciable affect when the length scale of the wave and the geometry are similar Visible light: 400nm – 700nm Sound waves: 17mm – 17m

33. Interference

35. Main Strategy For any kind of diffraction, the game is always about counting up phase shifts; these can be expressed in terms of angles or wavelengths – Angles Constructive Interference: Even multiples of π Destructive Interference: Odd multiples of π – Wavelengths Constructive Interference: Integer multiples of λ Destructive Interference: Odd half-integer multiples of λ

36. Practice Problem

40. Practice Problems

41. Practice Problem

44. Practice Problems Answer: E

45. Practice Problem

51. Practice Problems

52. Practice Problem

56. Practice Problems

57. Practice Problem