1. PHYS 241 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 Begin by drawing free body diagrams “Play” around with the problem Take fifteen to twenty minutes before the exam to relax… no studying.

4. Concepts Electricity – Gradient – Potential Energy – Potential – Capacitance Circuits – Current – Resistance/Resistivity – Kirchoff’s Rules Magnetism – Magnetic Fields – Magnetostatics – Electrodynamics

5. Gradient Situational: Cartesian Coordinates

6. Potential Energy Universal Situational

7. Potential

9. Situational

10. Potential

11. Word of caution: – Potential is not the same as potential energy, but they are intimately related – Electrostatic potential energy is not the same as potential energy of a particle. The former is the work to construct the entire configuration, while the later is the work required to bring that one particle in from infinity – There is no physical meaning to a potential, only difference in potential matter. This means that you can assign any point as a reference point for the potential – The potential must be continuous

12. Tying it Together Electric Field Potential Potential Energy Electric Force Multiply by q Vectors Scalars

13. Analogies with Gravity Electricity and magnetism can feel very abstract because we don’t usually recognize how much we interact with these forces There are many similarities between gravitational and electric forces The major difference is that the electric force can be repulsive Gravity even has a version of Gauss’s law ChargeForceFieldPE Electricityq Gravitym

14. Capacitance

16. Situational: Assumes steady fields Assumes uniform dielectric

17. Capacitance The permittivity of free space has no physical meaning It merely changes physical quantities into their appropriate SI units Physical UnitsSI Units LengthFarads Length/ChargeVolts Length^2/Charge^2Newtons Length/Charge^2Joules

18. Capacitance

20. Capacitors are in equilibrium – Series: when they have the same charge – Parallel: when they have the same voltage

21. Current

22. Resistance

23. Resistivity

24. Kirchoff’s Rules

25. General Procedure: – Choose loops so that every branch is covered by at least one loop – Choose current directions in each branch – this does not have to correspond to the direction of your loop – Write down each loop/node equation and solve using method of your choice. You need as many independent equations as you have currents to solve.

26. Kirchoff’s Rules The most common errors in applying Kirchoff’s rules are sign errors Voltage Source Resistor (Black arrows denote a positive change in voltage; red negative) Current

27. Capacitors and Inductors Capacitors and inductors act like mirrors of one another CapacitorInductor Proportionality Energy Charging Discharging Voltage

28. Kirchoff’s Rules

29. General Procedure: – Choose loops so that every branch is covered by at least one loop – Choose current directions in each branch – this does not have to correspond to the direction of you loop – Write down each loop and node equation and solve using method of your choice. You need as many independent equations as you have currents to solve.

30. Kirchoff’s Rules The most common errors in applying Kirchoff’s rules are sign errors Voltage Source Resistor Current

31. Right-Hand Rule and the Cross Product

33. Magnetic Fields

34. Lorentz Force (cont.) – Why should I care? Forces describe the acceleration a body undergoes The actual path the body takes in time can be found from the acceleration in two ways 1.Use integration to get the particle’s velocity as a function of time, then integrate again to gets its position 2.Kinematic equations (the result when method 1. is applied in the case of constant acceleration) This along with Maxwell’s equations describe all electromagnetic phenomena

35. Magnetostatics Electrostatics vs Magnetostatics – When we were talking about electrical phenomenon earlier in the course, we assumed we were at an equilibrium so no charges were moving – For our study of magnetism we will assume that our current is steady (or at least not varying rapidly) and that we are not too far away from our magnetic field source – Note that the principle of superposition is valid in both of these approximations

36. Magnetic Moment What does it tell me? – How a current loop or magnet responds to an external magnetic field Why should I care? – This drastically simplifies your calculations – You end up treating it like an electric dipole WireMagnetic Moment Torque Potential Energy

37. Biot-Savart Law

38. When running a Biot-Savart Law integral, it often becomes crucial to draw a picture to make sure you get the cross product correct FYI: If the magnetostatic approximation fails you would have to use the equation below!

39. Gauss’s Law for Magnetism

40. Why should I care? – Gauss’s law gives you important information about the shape of magnetic field lines – Essentially, magnetic lines of flux are loops and they never converge on or diverge from a point Note: when there are no currents flowing, we can use the concept of magnetic “charge” to solve problems, but this is a theoretical tool only

41. Ampere’s Law

42. Although this isn’t called Gauss’s law, this idea functions much like Gauss’s law for electric fields. This means that all the details about Gauss’s law apply here – You must use a closed loop – The current is that which is enclosed by the loop: this plays the analog as the source of a magnetic field – A line integral is a sum: Just because it evaluates to zero, does not mean that the magnetic field is zero – You must already know something about the magnetic field prior to applying Ampere’s Law

43. Practice Problems

44. Practice Problem

49. Practice Problems

52. Quiz Questions Remember: the negative charge Flips the direction of the force Relative to the cross product

53. Quiz Questions

55. Practice Problems

57. Quiz Question