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Fundamental Physics II

PETROVIETNAM UNIVERSITY FACULTY OF FUNDAMENTAL SCIENCES. Fundamental Physics II. Pham Hong Quang E-mail: quangph@pvu.edu.vn. Vungtau , 2013. Chapter 4. Electromagnetic Induction and Electromagnetic Wave. 4.1 Faraday law.

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Fundamental Physics II

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  1. PETROVIETNAM UNIVERSITY FACULTY OF FUNDAMENTAL SCIENCES

    Fundamental Physics II

    Pham Hong Quang E-mail: quangph@pvu.edu.vn Vungtau, 2013
  2. Chapter 4 Electromagnetic Induction and Electromagnetic Wave Pham Hong QuangFaculty of Fundamental Sciences
  3. 4.1 Faraday law Almost 200 years ago, Faraday looked for evidence that a magnetic field would induce an electric current with this apparatus: He found no evidence when the current was steady, but did see a current induced when the switch was turned on or off. Pham Hong QuangFaculty of Fundamental Sciences
  4. 4.1 Faraday law A changing magnetic field induces an emf. Pham Hong QuangFaculty of Fundamental Sciences
  5. 4.1 Faraday law Faraday’s Law of Induction; Lenz’s Law The induced emf in a wire loop is proportional to the rate of change of magnetic flux through the loop. Magnetic flux: Unit of magnetic flux: weber, Wb. 1 Wb = 1 T·m2 The magnetic flux is analogous to the electric flux – it is proportional to the total number of lines passing through the loop. Pham Hong QuangFaculty of Fundamental Sciences
  6. 4.1 Faraday law Faraday’s law of induction: The minus sign gives the direction of the induced emf: A current produced by an induced emf moves in a direction so that the magnetic field it produces tends to restore the changed field. Pham Hong QuangFaculty of Fundamental Sciences
  7. 4.1 Faraday law Magnetic flux will change if the area of the loop changes: Pham Hong QuangFaculty of Fundamental Sciences
  8. 4.1 Faraday law Magnetic flux will change if the angle between the loop and the field changes: Pham Hong QuangFaculty of Fundamental Sciences
  9. 4.1 Faraday law This image shows another way the magnetic flux can change: Pham Hong QuangFaculty of Fundamental Sciences
  10. 4.2 Application of Faraday’s law Electric Generators A generator is the opposite of a motor – it transforms mechanical energy into electrical energy. This is an ac generator: The axle is rotated by an external force such as falling water or steam. The brushes are in constant electrical contact with the slip rings. Pham Hong QuangFaculty of Fundamental Sciences
  11. 4.2 Application of Faraday’s law A sinusoidal emf is induced in the rotating loop (N is the number of turns, and A the area of the loop): Pham Hong QuangFaculty of Fundamental Sciences
  12. 4.2 Application of Faraday’s law Transformers and Transmission of Power A transformer consists of two coils, either interwoven or linked by an iron core. A changing emf in one induces an emf in the other. The ratio of the emfs is equal to the ratio of the number of turns in each coil: Pham Hong QuangFaculty of Fundamental Sciences
  13. 4.2 Application of Faraday’s law This is a step-up transformer – the emf in the secondary coil is larger than the emf in the primary: Energy must be conserved; therefore, in the absence of losses, the ratio of the currents must be the inverse of the ratio of turns: Pham Hong QuangFaculty of Fundamental Sciences
  14. 4.2 Application of Faraday’s law Transformers work only if the current is changing; this is one reason why electricity is transmitted as ac. Pham Hong QuangFaculty of Fundamental Sciences
  15. 4.2 Application of Faraday’s law This microphone works by induction; the vibrating membrane induces an emf in the coil Pham Hong QuangFaculty of Fundamental Sciences
  16. 4.2 Application of Faraday’s law Differently magnetized areas on an audio tape or disk induce signals in the read/write heads. Pham Hong QuangFaculty of Fundamental Sciences
  17. 4.3 Inductance Mutual inductance: a changing current in one coil will induce a current in a second coil. And vice versa; note that the constant M, known as the mutual inductance, is the same: Pham Hong QuangFaculty of Fundamental Sciences
  18. 4.3 Inductance Unit of inductance: the henry, H. 1 H = 1 V·s/A = 1 Ω·s. A transformer is an example of mutual inductance. Pham Hong QuangFaculty of Fundamental Sciences
  19. 4.3 Inductance A changing current in a coil will also induce an emf in itself: Here, L is called the self-inductance. Pham Hong QuangFaculty of Fundamental Sciences
  20. 4.3 Inductance l N turns i B S The self-inductance of a coil Magnetic field inside the coil Magnetic flux through one turn Magnetic flux through N turns Pham Hong QuangFaculty of Fundamental Sciences
  21. 4.3 Inductance RL Circuits Close the switch to a. What happens? Write down the loop rule. Loop Rule: Sum of potentials =0 Solve this equation for the current i. Pham Hong QuangFaculty of Fundamental Sciences
  22. 4.3 Inductance Pham Hong QuangFaculty of Fundamental Sciences
  23. 4.4 Energy Stored in a Magnetic Field Just as we saw that energy can be stored in an electric field, energy can be stored in a magnetic field as well, in an inductor, for example. Start with Loop rule or Kirchoff’s Law I Solve it for e Multiply by i Rate at which energy is stored in the magnetic field of the coil Rate at which energy is delivered to circuit from the battery Rate at which energy is lost in resistor Pham Hong QuangFaculty of Fundamental Sciences
  24. 4.4 Energy Stored in a Magnetic Field Pham Hong QuangFaculty of Fundamental Sciences
  25. 4.4 Energy Stored in a Magnetic Field Now define the energy per unit volume The energy density formula is valid in general Pham Hong QuangFaculty of Fundamental Sciences
  26. 4.5 The Production of ElectromagneticWaves Electromagnetic fields are produced by oscillating charges. Pham Hong QuangFaculty of Fundamental Sciences
  27. 4.5 The Production of ElectromagneticWaves The previous image showed the electric field; a magnetic field is also generated, perpendicular both to the electric field and to the direction of propagation. The electric field produced by an antenna connected to an ac generator propagates away from the antenna, analogous to a wave on a string moving away from your hand as you wiggle it up and down. Pham Hong QuangFaculty of Fundamental Sciences
  28. 4.5 The Production of ElectromagneticWaves An electromagnetic wave propagating in the positive x direction, showing the electric and magnetic fields: The direction of propagation and the directions of the electric and magnetic fields in an electromagnetic wave can be determined using a right-hand rule: Point the fingers of your right hand in the direction of E, curl your fingers toward B, and your thumb will point in the direction of propagation. Pham Hong QuangFaculty of Fundamental Sciences
  29. 4.6 The Propagation of ElectromagneticWaves All electromagnetic waves propagate through a vacuum at the same rate: c=3.00 x 108 m/s In materials, such as air and water, light slows down, but at most to about half the above speed. Pham Hong QuangFaculty of Fundamental Sciences
  30. 4.6 The Propagation of ElectromagneticWaves The value of the speed of light is given by electromagnetic theory; it is: This is a very large speed, but on an astronomical scale, it can take light a long time to travel from one star to another. Astronomical distances are often measured in light-years – the distance light travels in a year. Pham Hong QuangFaculty of Fundamental Sciences
  31. 4.6 The Propagation of ElectromagneticWaves The Doppler effect applies to electromagnetic waves as well as to sound waves. The speed of the waves in vacuum does not change, but as the observer and source move with respect to one another, the frequency does change. Pham Hong QuangFaculty of Fundamental Sciences
  32. 4.7 The Electromagnetic Spectrum Because all electromagnetic waves have the same speed in vacuum, the relationship between the wavelength and the frequency is simple: The full range of frequencies of electromagnetic waves is called the electromagnetic spectrum. Pham Hong QuangFaculty of Fundamental Sciences
  33. 4.7 The Electromagnetic Spectrum Radio waves are the lowest-frequency electromagnetic waves that we find useful. Radio and television broadcasts are in the range of 106 Hz to 109 Hz. Microwaves are used for cooking and also for telecommunications. Microwave frequencies are from 109 Hz to 1012 Hz, with wavelengths from 1 mm to 30 cm. Pham Hong QuangFaculty of Fundamental Sciences
  34. 4.7 The Electromagnetic Spectrum Infrared waves are felt as heat by humans. Remote controls operate using infrared radiation. The frequencies are from 1012 Hz to 4.3 x 1014 Hz. Visible light has a fairly narrow frequency range, from 4.3 x 1014 Hz (red) to 7.5 x 1014 Hz (violet). Ultraviolet light starts with frequencies just above those of visible light, from 7.5 x 1014 Hz to 1017 Hz. X-rays have higher frequencies still, from 1017 Hz to 1020 Hz. They are used for medical imaging. Pham Hong QuangFaculty of Fundamental Sciences
  35. 4.7 The Electromagnetic Spectrum Gamma rays have the highest frequencies of all, above 1020 Hz. These rays are extremely energetic, and are produced in nuclear reactions. They are destructive to living cells and are therefore used to destroy cancer cells and to sterilize food. Pham Hong QuangFaculty of Fundamental Sciences
  36. 4.8 Energy in Electromagnetic Waves The energy density in an electric field is: And in a magnetic field: Therefore, the total energy density of an electromagnetic wave is: Pham Hong QuangFaculty of Fundamental Sciences
  37. 4.8 Energy in Electromagnetic Waves It can be shown that the energy densities in the electric and magnetic fields are equal: Pham Hong QuangFaculty of Fundamental Sciences
  38. 4.8 Energy in Electromagnetic Waves The energy a wave delivers to a unit area in a unit time is called the intensity. Pham Hong QuangFaculty of Fundamental Sciences
  39. 4.9 Polarization The polarization of an electromagnetic wave refers to the direction of its electric field. Pham Hong QuangFaculty of Fundamental Sciences
  40. 4.9 Polarization Polarized light has its electric fields all in the same direction. Unpolarized light has its electric fields in random directions. Pham Hong QuangFaculty of Fundamental Sciences
  41. 4.9 Polarization A beam of unpolarized light can be polarized by passing it through a polarizer, which allows only a particular component of the electric field to pass through. Here is a mechanical analog: Pham Hong QuangFaculty of Fundamental Sciences
  42. 4.9 Polarization A polarizer will transmit the component of light in the polarization direction: Pham Hong QuangFaculty of Fundamental Sciences
  43. 4.9 Polarization Since the intensity of light is proportional to the square of the field, the intensity of the transmitted beam is given by the Law of Malus: The light exiting from a polarizer is polarized in the direction of the polarizer. Pham Hong QuangFaculty of Fundamental Sciences
  44. 4.9 Polarization If an unpolarized beam is passed through a polarizer, the transmitted intensity is half the initial intensity. Pham Hong QuangFaculty of Fundamental Sciences
  45. 4.9 Polarization A polarizer and an analyzer can be combined Pham Hong QuangFaculty of Fundamental Sciences
  46. 4.9 Polarization LCDs use liquid crystals, whose direction of polarization can be rotated depending on the voltage across them Pham Hong QuangFaculty of Fundamental Sciences
  47. Thank you! Nguyen Van A 47PetroVietnam University
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