1 / 58

Electricity and Magnetism

Electricity and Magnetism. Course PA113 – Unit 3. UNIT 3 – Introductory Lecture. The Magnetic Field Chapter 2 8 Sources of the Magnetic Field Chapter 2 9. Importance of Magnetic Fields. Practical Uses Electric motors, Loud speakers, Navigation (Earth’s magnetic field)

bayard
Télécharger la présentation

Electricity and Magnetism

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Electricity and Magnetism Course PA113 – Unit 3

  2. UNIT 3 – Introductory Lecture • The Magnetic Field • Chapter 28 • Sources of the Magnetic Field • Chapter 29

  3. Importance of Magnetic Fields • Practical Uses • Electric motors, Loud speakers, Navigation (Earth’s magnetic field) • In Experimental Physics • Mass spectrometers, Particle accelerators, Plasma confinement • In the Universe • Stars (e.g. the Sun), Interstellar space, Intergalactic structure, Jets

  4. Importance of Magnetic Fields

  5. Importance of Magnetic Fields • Units – SI Tesla (T) = (N C-1)/(m s-1) or N A-1 m -1 • 1 Gauss (G) = 10-4 T • Examples • Terrestrial B field ~ 4x10-5 T • Solenoid ~ 10-3 T • Permanent magnet ~ 10-1 T • Atomic interactions ~ 10 T • Superconducting magnet ~ 102 T • White dwarfs ~ 102 - 103 T • Neutron stars < 108 T

  6. Ch28 – The Magnetic Field • 28-1 Force exerted by a Magnetic Field • 28-2 Motion of a point charge in a Magnetic Field • 28-3 Torques on current loops and magnets • 28-4 The Hall Effect

  7. Vector Notation • The DOT product • The CROSS product

  8. 28-1 The Force Exerted by a Magnetic Field • Key Concept – Magnetic fields apply a force to moving charges Current element

  9. 28-1 The Force Exerted by a Magnetic Field

  10. Representation of Magnetic Field • Like electric field, can be represented by field lines • Field direction indicated by direction of lines • Field strength indicated by density of lines • But, unlike electric field • Magnetic field lines perpendicular to force • No isolated magnetic poles, so no points in space where field lines begin or end

  11. 28-2 Motion of a Point Charge in a Magnetic Field • Key Concept – Force is perpendicular to field direction and velocity • Therefore, magnetic fields do no work on particles • There is no change in magnitude of velocity, just direction

  12. Motion of a Point Charge in a Magnetic Field

  13. 28-2 Motion of a Point Charge in a Magnetic Field • Radius of circular orbit • Cyclotron period • Cyclotron frequency

  14. 28-3 Torques on Current Loops and Magnets • Key concept – a current loop experiences no net force in a uniform B field but does experience a torque

  15. Magnetic dipole moment 28-3 Torques on Current Loops and Magnets

  16. Integrate Zero at θ = 90o Potential Energy of a Magnetic Dipole in a Magnetic Field • Potential energy • Work done…..

  17. 28-4 The Hall Effect Vh = vdBw

  18. Ch29 – Sources of the Magnetic Field • 29-1 The Magnetic Field of moving point charges • 29-2 The Magnetic Field of Currents • Biot-Savart Law • 29-3 Gauss’ Law for Magnetism • 29-4 Ampère’s Law • 29-5 Magnetism in matter

  19. 29-1The Magnetic Field of Moving Point Charges • Point charge q moving with velocity v produces a field B at point P μo= permeability of free space μo= 4 x 10-7 T·m·A-1

  20. 29-2 The Magnetic Field of Currents: The Biot-Savart Law • Key concept – current as a series of moving charges – replace qv by Idl Add each element to get total B field

  21. Magnetic flux 29-3 Gauss’ Law for Magnetism • Key concept – The net flux of magnetic field lines through a closed surface is zero (i.e. no magnetic monopoles)

  22. 29-3 Gauss’ Law for Magnetism Electric dipole Magnetic dipole (or current loop)

  23. 29-4 Ampère’s Law • Key concept – like Gauss’ law for electric field, uses symmetry to calculate B field around a closed curve C N.B. This version assumes the currents are steady

  24. 29-5 Magnetism in Matter • Magnetization, M = m Bapp/0 • m is the magnetic susceptibility • Paramagnetic • M in same direction as B, dipoles weakly add to B field (small +ve m ) • Diamagnetic • M in opposite direction to B, dipoles weakly oppose B field (small -ve m ) • Ferromagnetic • Large +ve m, dipoles strongly add to B-field. Can result in permanent magnetic field in material.

  25. End of lecture 1

  26. Electricity and Magnetism Course 113 – Unit 3

  27. UNIT 3 – Problem solving Lecture • The Magnetic Field • Chapter 28 • Sources of the Magnetic Field • Chapter 29

  28. Problem Solving • Read the book!!!!! • Look at some examples • Try out some questions • Draw a diagram – include vector nature of the field (r and v or dl )

  29. You must know how to… • Calculate force on a moving charge • Or current element • Understand the properties of a dipole • Torque and magnetic moment • Calculate the B field using • The Biot-Savart law • Ampère’s Law • Understand Gauss’ Law for Magnetism

  30. 29-2 Example – the Biot-Savart Law applied to a current loop

  31. Field due to a current loop

  32. Field due to a current loop

  33. 2πR Field due to a current loop

  34. Magnetic field lines of 2 loops

  35. Many loops – a solenoid

  36. The B field in a very long solenoid Can use the Biot-Savart Law or Ampère’s Law Length L N turns n = N/L Radius R Current I di=nIdx Field in a very long solenoid: B =0nI

  37. Field around and inside a wire Classic example of the use of Ampère’s Law

  38. Direction of field around a wire

  39. End of lecture 2

  40. Electricity and Magnetism Course 113 – Unit 3

  41. UNIT 3 – Follow-up Lecture • The Magnetic Field • Chapter 28 • Sources of the Magnetic Field • Chapter 29

  42. Ch28 – The Magnetic Field • 28-1 Force exerted by a Magnetic Field • 28-2 Motion of a point charge in a Magnetic Field • 28-3 Torques on current loops and magnets • 28-4 The Hall Effect

  43. 28-1 The Force Exerted by a Magnetic Field • Key Concept – Magnetic fields apply a force to moving charges Current element

  44. 28-2 Motion of a Point Charge in a Magnetic Field • Radius of circular orbit • Cyclotron period • Cyclotron frequency

  45. Magnetic dipole moment 28-3 Torques on Current Loops and Magnets

  46. Ch29 – Sources of the Magnetic Field • 29-1 The Magnetic Field of moving point charges • 29-2 The Magnetic Field of Currents • Biot-Savart Law • 29-3 Gauss’ Law for Magnetism • 29-4 Ampère’s Law • 29-5 Magnetism in matter

  47. 29-2 The Magnetic Field of Currents: The Biot-Savart Law • Key concept – current as a series of moving charges – replace qv by Idl Add each element to get total B field

  48. Magnetic flux 29-3 Gauss’ Law for Magnetism • Key concept – The net flux of magnetic field lines through a closed surface is zero (i.e. no magnetic monopoles)

  49. 29-4 Ampère’s Law • Key concept – like Gauss’ law for electric field, uses symmetry to calculate B field around a closed curve C N.B. This version assumes the currents are steady

  50. Example

More Related