1. Fundamental Physics II PETROVIETNAM UNIVERSITY FACULTY OF FUNDAMENTAL SCIENCES Vungtau, 2013 Pham Hong Quang E-mail: quangph@pvu.edu.vn

2. Chapter 4 Pham Hong Quang Faculty of Fundamental Sciences 2 Electromagnetic Induction and Electromagnetic Wave

3. 4.1 Faraday law Pham Hong Quang Faculty of Fundamental Sciences 3 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.

4. 4.1 Faraday law Pham Hong Quang Faculty of Fundamental Sciences 4 A changing magnetic field induces an emf.

5. 4.1 Faraday law Pham Hong Quang Faculty of Fundamental Sciences 5 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·m 2 The magnetic flux is analogous to the electric flux – it is proportional to the total number of lines passing through the loop.

6. 4.1 Faraday law Pham Hong Quang Faculty of Fundamental Sciences 6 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.

7. 4.1 Faraday law Pham Hong Quang Faculty of Fundamental Sciences 7 Magnetic flux will change if the area of the loop changes:

8. 4.1 Faraday law Pham Hong Quang Faculty of Fundamental Sciences 8 Magnetic flux will change if the angle between the loop and the field changes:

9. 4.1 Faraday law Pham Hong Quang Faculty of Fundamental Sciences 9 This image shows another way the magnetic flux can change:

10. 4.2 Application of Faraday’s law Pham Hong Quang Faculty of Fundamental Sciences 10 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.

11. 4.2 Application of Faraday’s law Pham Hong Quang Faculty of Fundamental Sciences 11 A sinusoidal emf is induced in the rotating loop ( N is the number of turns, and A the area of the loop):

12. 4.2 Application of Faraday’s law Pham Hong Quang Faculty of Fundamental Sciences 12 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:

13. 4.2 Application of Faraday’s law Pham Hong Quang Faculty of Fundamental Sciences 13 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:

14. 4.2 Application of Faraday’s law Pham Hong Quang Faculty of Fundamental Sciences 14 Transformers work only if the current is changing; this is one reason why electricity is transmitted as ac.

15. 4.2 Application of Faraday’s law Pham Hong Quang Faculty of Fundamental Sciences 15 This microphone works by induction; the vibrating membrane induces an emf in the coil

16. 4.2 Application of Faraday’s law Pham Hong Quang Faculty of Fundamental Sciences 16 Differently magnetized areas on an audio tape or disk induce signals in the read/write heads.

17. 4.3 Inductance Pham Hong Quang Faculty of Fundamental Sciences 17 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:

18. 4.3 Inductance Pham Hong Quang Faculty of Fundamental Sciences 18 Unit of inductance: the henry, H. 1 H = 1 V·s/A = 1 Ω ·s. A transformer is an example of mutual inductance.

19. 4.3 Inductance Pham Hong Quang Faculty of Fundamental Sciences 19 A changing current in a coil will also induce an emf in itself: Here, L is called the self-inductance.

20. 4.3 Inductance Pham Hong Quang Faculty of Fundamental Sciences 20 S iB l N turns The self-inductance of a coil Magnetic field inside the coil Magnetic flux through one turn Magnetic flux through N turns

21. 4.3 Inductance Pham Hong Quang Faculty of Fundamental Sciences 21 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. RL Circuits

22. 4.3 Inductance Pham Hong Quang Faculty of Fundamental Sciences 22

23. 4.4 Energy Stored in a Magnetic Field Pham Hong Quang Faculty of Fundamental Sciences 23 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. Rate at which energy is delivered to circuit from the battery Rate at which energy is lost in resistor Rate at which energy is stored in the magnetic field of the coil Start with Loop rule or Kirchoff’s Law I Solve it for  Multiply by i

24. 4.4 Energy Stored in a Magnetic Field Pham Hong Quang Faculty of Fundamental Sciences 24

25. 4.4 Energy Stored in a Magnetic Field Pham Hong Quang Faculty of Fundamental Sciences 25 Now define the energy per unit volume The energy density formula is valid in general

26. 4.5 The Production of Electromagnetic Waves Pham Hong Quang Faculty of Fundamental Sciences 26 Electromagnetic fields are produced by oscillating charges.

27. 4.5 The Production of Electromagnetic Waves Pham Hong Quang Faculty of Fundamental Sciences 27 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.

28. 4.5 The Production of Electromagnetic Waves Pham Hong Quang Faculty of Fundamental Sciences 28 An electromagnetic wave propagating in the positive x direction, showing the electric and magnetic fiel ds: 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.

29. 4.6 The Propagation of Electromagnetic Waves Pham Hong Quang Faculty of Fundamental Sciences 29 All electromagnetic waves propagate through a vacuum at the same rate: c=3.00 x 10 8 m/s In materials, such as air and water, light slows down, but at most to about half the above speed.

30. 4.6 The Propagation of Electromagnetic Waves Pham Hong Quang Faculty of Fundamental Sciences 30 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.

31. 4.6 The Propagation of Electromagnetic Waves Pham Hong Quang Faculty of Fundamental Sciences 31 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.

32. 4.7 The Electromagnetic Spectrum Pham Hong Quang Faculty of Fundamental Sciences 32 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.

33. 4.7 The Electromagnetic Spectrum Pham Hong Quang Faculty of Fundamental Sciences 33 Radio waves are the lowest-frequency electromagnetic waves that we find useful. Radio and television broadcasts are in the range of 10 6 Hz to 10 9 Hz. Microwaves are used for cooking and also for telecommunications. Microwave frequencies are from 10 9 Hz to 10 12 Hz, with wavelengths from 1 mm to 30 cm.

34. 4.7 The Electromagnetic Spectrum Pham Hong Quang Faculty of Fundamental Sciences 34 Infrared waves are felt as heat by humans. Remote controls operate using infrared radiation. The frequencies are from 10 12 Hz to 4.3 x 10 14 Hz. Visible light has a fairly narrow frequency range, from 4.3 x 10 14 Hz (red) to 7.5 x 10 14 Hz (violet). Ultraviolet light starts with frequencies just above those of visible light, from 7.5 x 10 14 Hz to 10 17 Hz. X-rays have higher frequencies still, from 10 17 Hz to 10 20 Hz. They are used for medical imaging.

35. 4.7 The Electromagnetic Spectrum Pham Hong Quang Faculty of Fundamental Sciences 35 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.

36. 4.8 Energy in Electromagnetic Waves Pham Hong Quang Faculty of Fundamental Sciences 36 The energy density in an electric field is: And in a magnetic field: Therefore, the total energy density of an electromagnetic wave is:

37. 4.8 Energy in Electromagnetic Waves Pham Hong Quang Faculty of Fundamental Sciences 37 It can be shown that the energy densities in the electric and magnetic fields are equal:

38. 4.8 Energy in Electromagnetic Waves Pham Hong Quang Faculty of Fundamental Sciences 38 The energy a wave delivers to a unit area in a unit time is called the intensity.

39. 4.9 Polarization Pham Hong Quang Faculty of Fundamental Sciences 39 The polarization of an electromagnetic wave refers to the direction of its electric field.

40. 4.9 Polarization Pham Hong Quang Faculty of Fundamental Sciences 40 Polarized light has its electric fields all in the same direction. Unpolarized light has its electric fields in random directions.

41. 4.9 Polarization Pham Hong Quang Faculty of Fundamental Sciences 41 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:

42. 4.9 Polarization Pham Hong Quang Faculty of Fundamental Sciences 42 A polarizer will transmit the component of light in the polarization direction:

43. 4.9 Polarization Pham Hong Quang Faculty of Fundamental Sciences 43 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.

44. 4.9 Polarization Pham Hong Quang Faculty of Fundamental Sciences 44 If an unpolarized beam is passed through a polarizer, the transmitted intensity is half the initial intensity.

45. 4.9 Polarization Pham Hong Quang Faculty of Fundamental Sciences 45 A polarizer and an analyzer can be combined

46. 4.9 Polarization Pham Hong Quang Faculty of Fundamental Sciences 46 LCDs use liquid crystals, whose direction of polarization can be rotated depending on the voltage across them

47. 47 Nguyen Van A 47 PetroVietnam University Thank you!