Exam 3 Lectures Magnetism

1. Exam 3 LecturesMagnetism

2. Definitions • Magnetic field—The vector field a magnet produces all around itself to interact with its environment (produces force) • Tesla—the unit of the magnetic field • Permanent magnets—have a permanent magnetic field without outside influences • Electromagnets—magnets, which have a magnetic field in the presence of a current but not without it

3. More Definitions • Monopoles—magnetic charges (not found in nature) • North pole—end from which field lines emerge • South pole—end where field lines enter. • Crossed fields—an E field and B field present that are perpendicular to each other

4. Magnetic Fields • Produced by: • Moving electrically charged particles • Elementary particles (such as electrons) have an intrinsic magnetic field around them—basic characteristic of such particles • On the earth the south magnetic pole is close to the north geographic pole, and the north magnetic pole is close to the south geographic pole • A C shaped magnet is used to get a uniform magnetic field in experiments

6. Opposite magnetic poles attract each other Like magnetic poles repel each other

7. Magnetic Field Lines and Magnetic Fields • The direction of the magnetic B field at any point on a B field line is in the direction of the tangent to the B field line. • The spacing of the lines represents the magnitude of the B field. The B field is stronger where the B field lines are closer together. • The B field lines all pass through the magnet forming closed loops: they go in one side and out the other

9. Force a moving charged particle feels from an external magnetic field Must use the right hand rule for direction

11. Differences Between Electric and Magnetic Forces • The electric force acts in the direction of the E field, whereas the magnetic force acts perpendicular to the B field. • The electric force acts on a charged particle whether or not it is moving, whereas the magnetic force acts on a charged particle only if it is moving. • The electric force does work in displacing a charged particle, whereas the magnetic force does no work when a charged particle is displaced

12. Circulating Charged Particles • Important that force is perpendicular to velocity; therefore force can change direction but not magnitude of velocity • Particles under the influence of the magnetic force undergo uniform circular motion

13. Circulating Charged Particles cont • If velocity of charged particle has component parallel to magnetic field, the particle will move in a helical path • Parallel component – pitch of helix • Perpendicular component – radius of helix

15. Circulating charges have uses and examples in nature: • The magnetic bottles used in some experiments • Cyclotrons • Synchrotrons

16. The van Allen belts of the earth

18. Current Carrying Wire • Current consists of charges moving along the wire

19. same direction of force if we assume positive or negative charge carriers

20. Torque

21. Torque tends to rotate the loop so that A is rotated into the direction of B

22. Potential Energy

23. Crossed Fields – Hall Effect • Charged particles moving through the conductor subject to an external B field – get a magnetic force acting on them. • Magnetic force deflects the charged particles in the direction of the force and makes them line up on one wall of the conductor. • One wall of the conductor is more negative and the other is more positive charge – electric field is set up. • Eventually electric force balances magnetic force and the charges are allowed to continue on their way. • One wall will be at a higher potential than the other. • By looking at the potential difference between the two walls the sign the charges may be determined

24. a) Shows the situation for which the charge carriers are negative b) Shows the situation for which the charge carriers are positive

25. Mass Spectrometer • Another use of crossed fields

26. Calculating Fields Comparison

27. Calculating Magnetic Field due to a Current • Magnetic fields are produced by moving charges (currents) • Biot Savart Law

30. Some Magnetic Fields • Long Straight Wire • Half a Long Straight Wire • Circular Arc of Wire

32. Force Between 2 Parallel Currents • Parallel currents attract, antiparallel currents repel

33. Ampere’s Law • This is a line integral to be integrated around a closed loop (Amperian loop) • To use Ampere’s Law • First decide which type of symmetry best complements the problem • Draw an Amperian loop (mathematical not real) reflecting the symmetry you chose around the current distribution through the point of interest.

34. Long Cylindrical Conductor

35. INSIDE linear OUTSIDE hyperbolic

36. Solenoid • Solenoid – a long tightly wound helical coil of wire

38. Toroid • Toroid – a solenoid bent into a doughnut shape

39. Definitions • Induced current—current produced in a loop by a changing magnetic field • Induced emf—work done per unit charge in producing a current. • Induction—process of producing current and emf • Faraday’s law of induction—an emf is induced in a loop when the number of magnetic field lines that pass through the loop changes. • Lenz’s law—an induced current has a direction such that the magnetic field due to the current opposes the change in magnetic field that induces the current. The direction of the induced emf is the direction of the induced current

41. First of Two Experiments • Three discoveries: • Current appears only if there is relative motion between the loop and magnet • Faster motion between the loop and magnet produces greater current • Opposite motion of the magnet produces opposite direction of current

42. Second of Two Experiments • Current in a wire produces a magnet field • As the current increases the magnetic field increases • As the magnetic field increases a current appears.

43. Magnetic Flux • Units of magnetic flux is the Weber • Three terms and therefore three ways that flux can change with time

44. Induction – Faraday’s Law • Faraday’s Law – an emf is induced in a loop when the number of magnetic field lines passing through the loop changes • The negative only tells us direction and we will ignore it (unless I have a reason not to) • The number of field lines doesn’t matter, just the rate of change of the number of field lines determines the induced emf and current

45. Induction cont • Notice there are three terms and therefore three ways that flux can change: • The magnitude of the magnetic field can change • The area of the coil can change • The angle between the direction of the magnetic field and the coil can change

46. Lenz’s Law • An induced current has a direction such that the magnetic field due to the current opposes the change in the magnetic flux that induces the current • The direction of the induced emf is the direction of the induced current

49. Solving Problems • First know the direction of the external changing B field • Next note how the external B field is changing • Use the two rules below to determine the direction the induced B field must have • Test with to determine the direction of the induced current to give the appropriate direction of the induced B field • It must follow the two rules below: • If the external B field is increasing, the induced B field is in the opposite direction of the external B field • If the external B field is decreasing, the induced B field is in the same direction of the external B field

50. Energy Transfer • During induction thermal energy is produced by the work done to the system