PHYS 222 SI Exam Review 3/31/2013

1. PHYS 222 SI Exam Review3/31/2013

3. Answer: D

5. Answer: D,D

7. Answer: D,C

8. What to do to prepare • Review all clicker questions, but more importantly know WHY • Review quizzes • Make sure you know what all the equations do, and when to use them

9. SI Leader Secrets!Extra problems? Visit the website below to get past exams all the way back to 2001!! (Note: the link below has stuff that you wouldn’t otherwise see) http://course.physastro.iastate.edu/phys222/exams/ExamArchive222/exams/

10. These are all equations used for an RC circuit.

11. Used to find the charge Q on the capacitor in an RC circuit that initially has no charge and is slowly brought to a maximum charge . • What is

12. Used to find the charge Q on the capacitor in an RC circuit that initially has charge Q(0) and has been disconnected from the power source. • I(t) is used to find the current in the resulting circuit. As before,

13. Used to find the force on a point charge of charge q in an electric field E and magnetic field B. • Notice that the magnetic force is , and only exists if the charge is moving.

14. This is the differential form of the magnetic force on a length of wire carrying current. • Probably more useful in this form: • Note that if the wire and B field are pointing in the same direction, the force is zero.

15. is the magnetic flux through a closed surface. Ex: A uniform B field of 5 T goes through a circular loop of wire of radius 10 m, What is the magnetic flux? Ans:

16. Here, a charge of magnitude q and mass m is acted on by a constant B field. As a result, the charge moves in a circle of radius R and its tangential speed is v.

17. This is the equation for the magnetic dipole ( of a loop of current. • is a vector • As an example,if the radius is4 m and I=2,then up

18. This gives the torque on a magnetic dipole by a magnetic field. • Note that torque is zero if the magnetic dipole and the B field point in the same direction.

19. This gives the potential energy of a magnetic dipole in a magnetic field.

20. The equation for the magnetic field produced by a moving charge q at a speed v. • is just the distance away from the moving charge. • just means to use the right hand rule to determine which direction the magnetic field points.

21. Same equation as before, except that instead of a single point charge moving, we have a current I. • This equation is probably easier to use in its linear, non-differential form , • just means to use the right hand rule to determine which direction the magnetic field points.

22. Right-hand rule

23. This is the magnetic field a distance r away from an infinite straight wire carrying current I. • The direction of the field is given by the right hand rule.

24. This gives the force between two parallel wires. One wire carries current I, the other wire carries current I’. • If the currents are pointing in the same direction, the force is attractive. If they are opposite, the force is repulsive.

25. Is the force attractive or repulsive? • Answer: attractive.

26. I doubt you’d find a practical use for this equation in exam 2, because it really only says that the speed of light squared is equal to the inverse of the products of two constants.Cool, but not really something testable.

27. Let’s say you have a wire bent in a circle of radius a (in the picture it’s shown as R), with N turns. This equation gives the B field at the center of the circle a distance x above the center (if the circle is in the x-y plane, the variable x is the z coordinate). • The direction of the B field is given by the right hand rule, as discussed earlier.

28. This equation is really just a special case of the previous one. This is the B field at the center of the circle, in the plane.

29. Question: • In the picture does the B field produced by the current point into the page or out of the page?

30. Question: • In the picture does the B field produced by the current point into the page or out of the page? • Answer: Into the page.

31. This is the equation for the field inside of a solenoid. • Note that it is a uniform field(i.e. everywhere inside of the solenoid it’s the same). • Lowercase n is the turns per length.

32. This is sometimes known as Ampere’s law. • Can be used to derive many magnetic fields, for example this one: . (Field away from any infinite straight wire)

33. This equation is known by many names, including Faraday’s Law and Lenz’s Law, depending on who you talk to. • Basically it says that a current loop without a voltage or current source can have an induced voltage if there’s a changing magnetic flux inside the loop. • Note that the direction of the EMF is OPPOSITE the change in flux.

34. This is just another way of expressing the EMF. • Recall is the magnetic force, so here we’re sort of (there’s no q up there) saying that the path integral of the magnetic force is equal to the emf.

35. This just says that an induced E field is what causes the induced EMF seen in the earlier equation: • Notice how there’s an N missing in the equation up top. That’s because includes the N already, whereas in the bottom equation it doesn’t.

36. This is a copy of an equation we saw earlier, except that it includes the displacement current. • What is the displacement current? The equation is on the next page, but the physical meaning is that it’s not a true current, but rather a mathematical construction to deal with changes in electric flux.

37. Here’s the equation for displacement current.

38. One of the so-called “Maxwell’s Equations” • Also known as Gauss’s law. • Used to calculate the E fields for many common charge shapes, such as spheres and cylinders. (Theoretically can be used for complicated ones too, but that requires fancy mathematical software)

39. One of the so-called “Maxwell’s Equations” • Says that the magnetic flux through a closed, 3-D surface is always zero.

40. One of the so-called “Maxwell’s Equations” • This is basically the same as the induced EMF equation.

41. One of the so-called “Maxwell’s Equations” • This equation basically appears twice on the equation sheet.

42. If you have two loops of current with mutual inductance M, and a current i2is going through one of them, then an emf (voltage) is produced through the other one, which excites a current in that one.

43. If you have two loops of current with mutual inductance M, and a current i1 is going through one of them, then an emf (voltage) is produced through the other one, which excites a current in that one. • Basically the same idea as the last equation.

44. The definition of mutual inductance M. Use the side of the equation that is relevant. • Note that although it appears that M depends on current i, the fact of the matter is that M never depends on i because the i in the numerator cancels with the i in the denominator. • There is an i in the numerator because flux depends on B, and B depends on i.

45. This is the induced emf across an inductor. Note that the induced emf occurs opposite the change in current.

46. Definition of self-inductance L.

47. Current across an inductor in an LR circuit when you just start flowing current in the circuit.

48. Current across an inductor in an LR circuit when you just stop flowing current in the circuit.

49. The time constant in LR circuits.

50. Self inductance of a solenoid of n turns per length, of length L, and cross sectional area A.