PHYS 241 Exam Review

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. • Look for symmetries

4. Concepts • Circuits • Current • Resistance/Resistivity • Capacitors and Inductors • Kirchoff’s Rules • Magnetism • Magnetic Fields • Magnetostatics • Electrodynamics

5. Current • What does it tell me? • The amount of charge flowing through a boundary • The word “flow” implies there should be an equation similar to flux that describes this

6. Resistivity • The resistivity tells us how easy it is to push charge through a material, regardless of its dimensions • Resistivity depends on temperature and the temperature coefficient gives us this relationship measured relative to

7. Resistance • What does it tell me? • The ratio of the potential drop in the “direction” of the current and the current in a segment and is measured in ohms () • Essentially it is telling you how tough it is to push charge through an object • Why do I care? • All things have resistance so it is critical to understand how it affects electric current • The resistor is another one of our linear electronic components

8. Capacitors and Inductors • Capacitors and inductors act like mirrors of one another

9. Kirchoff’s Rules • Loop Rule • Based on conservation of energy • Node Rule • Based on conservation of charge

10. Kirchoff’s Rules 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.

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

12. Right-Hand Rule and the Cross Product • Cross product is perpendicularto BOTH of the vectors in theproduct • You sweep your hand from thefirst vector to the second throughthe smallest angle between • Measures how perpendiculartwo vectors are

13. Magnetic Fields • Lorentz Force • What does it tell me? • The force a charged particle experiences in an electromagnetic field • For a wire this becomes

14. Magnetic Fields • 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 • Use integration to get the particle’s velocity as a function of time, then integrate again to gets its position • 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

15. Magnetostatics • Electrostatics vsMagnetostatics • 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

16. 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

17. Biot-Savart Law • What does it tell me? • The magnetic field produced by a current in the magnetostatic approximation • Why should I care? • This is a fundamental physical principle derived from experimental data

18. Biot-Savart Law • 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!

19. Gauss’s Law for Magnetism • What does it tell me? • The net magnetic flux through a closed surface is zero • If you recall our discussion about electric flux, the net flux of a field through a closed surface is proportional to the total sources and sinks that are within the volume bounded by the surface • This means that there are NO magnetic charges

20. Gauss’s Law for Magnetism • 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

21. Ampere’s Law • What does it tell me? • A closed path integral of the magnetic field is proportional to the current that flows through the loop • Why should I care? • You can always use it to calculate the current within a region and when there is a HIGH of degree symmetry you can figure out the magnetic field

22. Ampere’s Law • 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

23. Electromotive Force (EMF) • What does it tell me? • The change in potential energy per unit charge an object has when moved along a path • It can also refer to the voltage measured across two terminals • Why do I care? • So far we have considered conservative electric fields which have scalar potentials • For non-conservative fields, the change in potential energy becomes path dependent and EMF is accounting for that

24. Electromotive Force (EMF) • 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: • This is not a force, it has units of volts • This is not a potential, the path taken matters very much

25. 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

26. Motional EMF

27. Farraday’s Law • Two earlier approximation schemes • Electrostatics • Stationary charges • Conducting charges at equilibrium • Magnetostatics • Steady Currents

28. Farraday’s Law • In electrodynamics we allow single charges to move • This causes time varying magnetic fields bringing Farraday’s law into effect

29. Farraday’s Law • 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

30. 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

31. 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

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