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The Magnetic Field

The Magnetic Field. Chapter 30. Magnetic Forces. Magnetic Force - A force present when an electric charge is in motion. A moving charge is said to produce a magnetic field . Magnetic fields exert forces on moving charges. Magnetic Fields. Represented by field lines . By definition:

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The Magnetic Field

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  1. The Magnetic Field Chapter 30

  2. Magnetic Forces • Magnetic Force - A force present when an electric charge is in motion. • A moving charge is said to produce a magnetic field . • Magnetic fields exert forces on moving charges.

  3. Magnetic Fields • Represented by field lines . • By definition: • or more commonly: • Where q is the angle between v and B.

  4. Magnetic Field Units • Standard Unit = Tesla (T) • 1 T = 1 N/A•m • 1 T = 104 gauss

  5. Force on Moving Charges • The diagram below shows a uniform magnetic field with several charges in motion. v v v v

  6. Force on Moving Charges • The magnitude of the force on each charge can be found by qvXB or qvBsinq. • The direction of the force is found by a right hand rule.

  7. Right Hand Rule • 1) Place your fingers in the direction of the velocity. • 2) Curl your fingers toward the direction of the field. You might need to turn your hand. • 3) Your thumb points in the direction of the force.

  8. Direction of Force v F F = 0 v F F v v

  9. Magnetic Field Lines • NOT lines of force. • Force on charges is not in the direction of the magnetic field. • Force is always perpendicular to the velocity of the charge. • Force is always perpendicular to the magnetic field. • RHR & LHR

  10. Permanent Magnets • Magnetic field lines point away from north poles • and toward south poles.

  11. Magnetic Flux • The amount of a magnetic field passing through a given area. • Proportional to the number of magnetic field lines which pass through an area.

  12. Magnetic Flux Maximum Flux A A A No Flux

  13. Flux Units • Weber • 1 Wb = 1 T/m2

  14. Gauss's Law for Magnetism • The magnetic flux through any closed surface must be zero. N S

  15. Example • Exercise 4

  16. homework • E 1, 2, 7

  17. Motion of Charges in a Magnetic Field • Two possible paths can result for the motion of the charge: • 1) If vo is perpendicular to B, a circular path will result. • 2) If vo is not perpendicular to B, the charge will travel in a spiral path.

  18. vo perpendicular to B

  19. vo at an angle to B

  20. Magnetic Bottle

  21. Van Allen Belts

  22. Motion of Charges • As a charge circles or spirals in a magnetic field, the radius of its path is dependent on the perpendicular component of its velocity.

  23. Mass Spectrometer

  24. Velocity Selector • Only allows charges with a specific velocity to pass through undeflected. • FB is opposite of FE • E is perpendicular to B

  25. Velocity Selector FE FB

  26. Velocity Selector • For a specific value of v, the electric force and the magnetic force will be equal to each other and opposite in direction. • FB = FE • qvB = qE • vB = E

  27. Current-Carrying Wire • Since a current is moving charges, a current-carrying wire experiences a force in a magnetic field. (B into screen) F X X X X X X X X X X X X X X X X

  28. Magnitude of Force

  29. Example • Exercise 14

  30. homework • E 19, 20

  31. Sources of Magnetic Fields Chapter 31

  32. Long, straight wire mo is equal to 4p x 10–7 T•m/A.

  33. Current Carrying Wire • Shape of the field is circular. • Concentric circles • The direction is given a Right Hand Rule: • Thumb in the direction of the current. • Curl your fingers and they give the direction of the field.

  34. Moving Charge + • v

  35. I B Wire • • • • • • • • • I x x x x x x x x x

  36. Parallel conductors • Each creates a magnetic field that produces a force on the other • Can calculate force per unit length • To find direction, use both right hand rules

  37. Definition of Ampere • Comes from force exerted by two parallel conductors • 1 A is the current necessary in each conductor (if 1 m apart) to produce a force of 2 x 10-7 N.

  38. Field of a circular loop or coil • At center of loop • Direction found with right hand rule – like current in straight wire

  39. Field of a Solenoid • Long Spring-like Coil • Uniform field in the interior:

  40. Examples • Exercises 1 and 7

  41. homework • E 2, 6, 10, 12

  42. Ampere’s Law • Like Gauss’s law I

  43. Long straight wire I

  44. Example • A wire has a radius of R and carries a current I that is uniformly distributed across its area. • Determine how to calculate the magnitude of the magnetic field inside and outside the conductor.

  45. R r Inside • The current inside a circle of radius r would be a fraction of the total current. • Same ratio as areas. • With total current, I:

  46. Outside • A circle of radius r, where r > R, encloses all the current. r R

  47. Example • Determine the field inside a solenoid

  48. Solenoid • Vertical sides – zero because B is perpendicular to sides • Side outside solenoid – if it is far away from the solenoid, B is zero

  49. Paramagnetic materials • Can become magnetized • An external magnetic field causes atoms to line up so their currents add to the external field

  50. Ferromagnetic materials • Atomic currents line up even when no external field is present • Permanent magnets

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