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Chapter 27

Chapter 27. Magnetic Field and Magnetic Forces. Goals for Chapter 27. Study magnets & forces they exert on each other Calculate force a magnetic field exerts on a moving charge Contrast magnetic field lines with electric field lines

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Chapter 27

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  1. Chapter 27 Magnetic Field and Magnetic Forces

  2. Goals for Chapter 27 • Study magnets& forces they exert on each other • Calculate force a magnetic field exerts on a moving charge • Contrast magneticfield lines with electric field lines • Analyze motion of a charged particle in a magnetic field

  3. Goals for Chapter 27 • See applications of magnetism in physics and chemistry • Analyze magnetic forces on current-carrying conductors • Study the behavior of current loops in a magnetic field

  4. Introduction • How does magnetic resonance imaging (MRI) allow us to see details in soft nonmagnetic tissue? • How can magnetic forces, which act only on moving charges, explain the behavior of a compass needle?

  5. Magnetic poles • Forces between magnetic poles mimic forces between charges.

  6. Magnetism and certain metals • BUT….either pole of a permanent magnet will attract a metal like iron??

  7. Magnetic field of the earth

  8. Magnetic monopoles • Breaking a bar magnet does not separate its poles • There is no experimental evidence for magnetic monopoles.

  9. Electric current and magnets • In 1820, Hans Oersted discovered that a current-carrying wire causes a compass to deflect. • This discovery revealed a connection between moving charge and magnetism.

  10. Electric current and magnets • We’ll find a RIGHT-HAND RULE applies to identify the direction of a magnetic field from a current-carrying wire! Right Thumb in direction of current Right Hand Fingers curl in direction of Magnetic field!

  11. Electric current and magnets • We’ll find a RIGHT-HAND RULE applies to identify the direction of a magnetic field from a current-carrying wire! Right Thumb in direction of current Right Hand Fingers curl in direction of Magnetic field!

  12. The magnetic field • A moving charge (or current) creates a magnetic field in the surrounding space.

  13. The magnetic field • Magnetic fields denoted with letter “B” • measured in Tesla or Gauss (10-7 Tesla)

  14. The magnetic field • Magnetic fields denoted with letter “B” • measured in Tesla or Gauss (10-4 Tesla) • Tesla = Newton-secondCoulomb-meter • Tesla = Newton/Amp-meter

  15. The magnetic field • A magnetic field exerts a force on any other moving charge - or current - that is present in the field.

  16. The magnetic force on a moving charge • The magnetic force on a moving charge q is perpendicular to both • the velocity vector direction of qand • the magnetic field. • The magnitude of the magnetic force is F = |q|vB sin.

  17. Magnetic force as a vector product • We can write the magnetic force as a vector product • The right-hand rule gives the direction of the force on a positivecharge.

  18. Magnetic force as a vector product • We can write the magnetic force as a vector product • The left-hand rule gives the direction of the force on a negativecharge.

  19. Equal velocities but opposite signs • Two charges of equal magnitude but opposite signs moving in the same direction in the same field will experience magnetic forces in opposite directions.

  20. Determining the direction of a magnetic field • A cathode-ray tube can be used to determine the direction of a magnetic field

  21. Magnetic force on a proton • Beam of protons (q =+1.6 x 10-19C) moves at 3.0 x 105 m/s through 2.0 Tesla field directed along z axis. Velocity direction is 30 degrees from the z axis in the x-y plane. Force on a proton?

  22. Magnetic field lines

  23. Magnetic field lines are not lines of force • It is important to remember that magnetic field lines are not lines of magnetic force.

  24. Magnetic flux

  25. Magnetic flux calculations • Flux through flat surface of area 3.0 cm2 = +0.90 milliWb. • What is B field and direction of A?

  26. Magnetic flux calculations • Flux through flat surface of area 3.0 cm2 = +0.90 milliWb. • What is B field and direction of A? • Flux FB = BA cos f = +0.90 milliWb • A = 3.0 cm2 = 3.0 x 10-4 m2 and f = 60° • B = 6.0 Teslas

  27. Motion of charged particles in a magnetic field • A charged particle in a magnetic field always moves with constant speed. • If velocity of particle is perpendicular to B field, particle moves in a circle of radius R = mv/|q|B. • Number of revolutions of particle per unit time is cyclotron frequency.

  28. Motion of charged particles in a magnetic field • F = qvB = mv2/R • w = v/R = qB/m • f = w/2p • Number of revolutions of particle per unit time is cyclotron frequency.

  29. Motion of charged particles in a magnetic field • Magnetron in Microwave Oven!

  30. Motion of charged particles in a magnetic field • Magnetron in Microwave Oven!

  31. Motion of charged particles in a magnetic field • Magnetron in Microwave Oven!

  32. Motion of charged particles in a magnetic field • Magnetron in Microwave Oven!

  33. Helical motion • If the particle has velocity components parallel to and perpendicular to the field, its path is a helix. • The speed and kinetic energy of the particle remain constant.

  34. A nonuniform magnetic field • Charges can be trapped in a magnetic bottle, which results from a non-uniform magnetic field. • Van Allen radiation belts act like a magnetic bottle, and produce aurora. These belts are due to the earth’s non-uniform field.

  35. Bubble chamber • Track of charged particles in a bubble chamber experiment.

  36. Velocity selector • A velocity selector uses perpendicular electric and magnetic fields to select particles of a specific speed from a beam. • Only particles having speed v = E/B pass through undeflected.

  37. Thomson’s e/m experiment • Measure ratio e/m for the electron.

  38. Mass spectrometer • A mass spectrometer measures the masses of ions. • The Bainbridge mass spectrometer first uses a velocity selector. Then the magnetic field separates the particles by mass.

  39. The magnetic force on a current-carrying conductor • Magnetic force on a moving positive charge in a conductor. • F = Ilx B = ILB sin f • dF = Idlx B for a segment dl • VECTORS! • I = scalar current (amps) • l = direction of current • B = direction of Mag. Field. • Magnetic force is perpendicular to the wire segment and the magnetic field.

  40. Magnetic force on a straight conductor • Example 27.7 • What is F on the segment? • What is the maximum possible force if it changes direction?

  41. Magnetic force on a curved conductor • Example 27.8 • What is the TOTAL magnetic force on this wire?

  42. Loudspeaker • Loudspeaker design. • If current in the voice coil oscillates, speaker cone oscillates at the same frequency.

  43. Force and torque on a current loop in B field • Net force on a current loop in a uniform magnetic field is zero. • But the net torque is not, in general, equal to zero.

  44. Force and torque on a current loop • Net force on a current loop in a uniform magnetic field is zero. • But the net torque is not, in general, equal to zero.

  45. Force and torque on a current loop • Net force on a current loop in a uniform magnetic field is zero. • But the net torque is not, in general, equal to zero.

  46. The direct-current motor • Direct-current motor.

  47. The direct-current motor • Direct-current motor.

  48. The direct-current motor • Direct-current motor.

  49. Magnetic moment • Magnetic torque and magnetic moment. • Right-hand rule to determine the direction of the magnetic moment of a current loop. • Potential energy of a magnetic dipole in a magnetic field.

  50. Magnetic torque and potential energy of a coil • Example 27.9

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