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  1. 1. Electric Fields<br />Section 2<br />Topic 1<br />
  2. 2. All matter is made up of atoms and molecules;<br />contain charged particles,<br />the proton and electron.<br />The charges on each are equal;<br />but opposite in sign.<br />Charges<br />
  3. 3. Fq1 and F q2<br /> Discovered a relationship between;<br />force (F),<br />distance (r) between the centres of the objects.<br />Coulomb’s Law<br />
  4. 4. Coulomb’s Law<br />The value of the constant is;<br />9.00 x 109 Nm2C-2, in a vacuum.<br />The constant is written as:<br /><ul><li>o is the permittivity in a vacuum or the ability to transmit electric force.</li></li></ul><li>Force is a vector and so must have a direction.<br />The force is along a line joining the two centres. <br />If charges are the same,<br />there is repulsion<br />If different,<br />there is attraction.<br />Coulomb’s Law states:<br />Coulomb’s Law<br />
  5. 5. The force acting between two charges q1 and q2;<br />who are separated by a distance d,<br />is directly proportional to the product of the charges,<br />and inversely proportional to the square of the distance between them.<br />The force is along the line joining the centres of the charges.<br />Coulomb’s Law<br />
  6. 6. This is similar to Newton’s law of universal gravitation:<br />Coulomb’s Law<br />
  7. 7. Coulomb’s & Newton’s Law<br />1. The interaction acts on both bodies.<br />2. Both forces act at a distance without the bodies touching.<br />3. Both directly proportional to the product of the properties causing the interaction.<br />4. Both inversely proportional to the distance between the bodies.<br />5. Forces are consistent with N III<br />
  8. 8. They are dissimilar in that:<br />1. Gravitation is a force of attraction only while charges can attract and repel.<br />2. The force between charges depends on the medium while gravity does not.<br />Coulomb’s & Newton’s Law<br />
  9. 9. As force is a vector we cannot algebraically add forces if there is more than one point charge present.<br />The law that we use to determine to total force is called the law of superposition.<br />When two or more point charges are present;<br />the total force is equal to,<br />the vector sum of the forces,<br />due to each of the other point charges.<br />Principle of Superposition<br />
  10. 10. To use this principle, follow the rules given below:<br />1. Draw a labelled diagram<br />Use coulombs law to determine the magnitude;<br />ignore the direction at this stage<br />3. Determine if the force is attractive or repulsive.<br />4. Repeat step 2 for any other combinations of charges.<br />5. Draw a vector diagram.<br />Principle of Superposition<br />
  11. 11. Find the resultant;<br />using Pythagoras theorem,<br />trigonometry<br />Determine the direction using trigonometry.<br />Principle of Superposition<br />
  12. 12. An electric field is a region in space where;<br />an object will experience a force due to,<br />its charge,<br />without the charges necessarily touching.<br />The Electric Field<br />
  13. 13. A diagram representing the relative strength of a field at any point can be drawn.<br />The lines drawn give,<br />direction of the force on a tiny positive charge.<br />If the charge were allowed to move,<br />the charge would move along the field line.<br />Lines of Electric Force<br />
  14. 14.  Rules for drawing electric field line diagrams.<br />1. Lines of electric force are always directed from positive to negative charges.<br />Lines of Electric Force<br />
  15. 15. Lines of electric force always start and end on a charged surface;<br />make an angle of 90o to that surface.<br />If the surface is curved;<br />construct a line at 90o to the tangent at that point.<br />Lines of Electric Force<br />
  16. 16. 3. Lines of electric force never cross.<br />There is no electric field inside a hollow conductor,<br />hence no lines of electric force exist.<br />Lines of electric force are found to concentrate;<br />at regions of high curvature on a conductor.<br />Lines of Electric Force<br />
  17. 17. The field may be strong enough<br />at the sharp point<br />to ionise the air.<br />Charges may then move away<br />from the conductor.<br />This is called Corona Discharge.<br />Lines of Electric Force<br />
  18. 18. Make sure that the number of field lines per unit area represents the field strength;<br />when close together the field is strong,<br />when far apart the field is weak.<br /> Where the field lines are parallel and equally spaced;<br />the field is said to be uniform.<br />Lines of Electric Force<br />
  19. 19. The field becomes curved;<br />or non uniform.<br />This is known as the end effect.<br />If the separation of the plates becomes too large;<br />the end effect encroaches on the region between the plates.<br />Lines of Electric Force<br />
  20. 20.
  21. 21. The electric field strength, E,<br />at a point in an electric field is given by the force, F,<br />acting on a unit positive charge placed at that point in the field.<br />Units for E are NC-1.<br />It is a vector with both magnitude and direction.<br />Electric Field Strength<br />
  22. 22. Consider two charges;<br />a fixed point charge q and a test charge qT,<br />separated by a vacuum by a distance r.<br />Coulomb’s law gives the force each feels;<br />directions will be opposite (NIII).<br />Derivation<br />
  23. 23. Can you derive<br />
  24. 24. If more than one charge exists in an electric field, the total field at any one point is;<br />the vector sum of the electric field strengths due to each charge.<br />Etotal = E1 + E2 + E3 + …….+ En<br />Electric Field Strength Due to Several Charges<br />
  25. 25. Electric Field Strength Due to Several Charges<br />Example<br />
  26. 26. Electric Field Strength Due to Several Charges<br />
  27. 27. There are five steps in the process.<br />The examination will focus only on corona discharge<br />Photocopiers & Laser Printers<br />
  28. 28. Step 1:Charging the Photoconductive Drum.<br />The drum has the special property of being an electrical insulator in the dark;<br />an electrical conductor when exposed to light.<br />Near the drum is a thin corona wire;<br />voltage of about 6000V between it and the drum,<br />extends for the length of the drum.<br />The polarity can vary depending on the design.<br />Photocopiers & Laser Printers<br />
  29. 29. The material used to coat the earthed aluminium drum;<br />3 - 15 cm in diameter,<br />to achieve this effect is commonly selenium.<br />Photocopiers & Laser Printers<br />
  30. 30. The electric field near the corona wire;<br />accelerates any ions in the atmosphere,<br />to high velocities.<br />They in turn collide with neutral atoms in the air;<br />knocking out some electrons.<br />These free electrons attach themselves to other neutral atoms.<br />From this process;<br />large amounts of positive and negative ions are formed,<br />as more and more collisions occur.<br />Photocopiers & Laser Printers<br />
  31. 31. These charged ions are attracted to either;<br />the corona wire,<br />or the drum.<br />On reaching the drum;<br />they charge the photoconductive coating uniformly,<br />as the drum rotates.<br />Photocopiers & Laser Printers<br />
  32. 32. Transferring the Toner to the Paper<br />The paper is charged the same sign as that on the drum;<br />using another corona wire,<br />called the transfer corona.<br />Photocopiers & Laser Printers<br />
  33. 33. So the paper does not cling to the drum, the extra charge on the paper is removed;<br />using another oppositely charged corona wire,<br />called the separation corona.<br />Photocopiers & Laser Printers<br />
  34. 34. Motion of Particles in Electric Fields<br />Section 2<br />Topic 2<br />
  35. 35. W = Fs<br />W = U<br />and U = qEd;<br />this can be equated to a gravitational field,<br />U = mgh.<br />d = distance the charge q;<br />is moved in a uniform field E.<br />W = qEd<br />V = Ed<br />W = qV <br />Electric Potential Difference<br />
  36. 36. The electric potential difference between two points in an electric field is;<br />the work done W in moving a positive test charge moved between the points,<br />provided that all other charges remain undisturbed.<br />The unit for electric potential difference is;<br />JC-1,<br />which is also known as;<br />volt (V).<br />Electric Potential Difference<br />
  37. 37. Change in potential = Ed<br />This is called the potential difference,<br />V.<br />V = Ed;<br />d = distance between two points;<br />parallel to the field.<br />More on P.D.<br />A more common way of expressing this is:<br />
  38. 38. If an electron is accelerated;<br />across a potential difference of 5 volts,<br />K.E. = 5 times its charge<br />i.e. 5 x 1.6 x 10-19 = 8.0 x 10-19J<br />One electron volt is the energy that an electron would gain;<br />if it were to accelerate,<br />across a potential difference of 1 volt.<br />Symbol for the electron volt is eV.<br />1 electron volt = 1.6 x 10-19 J<br />Electron Volt<br />
  39. 39. A charge that is free to move in a uniform electric field;<br />behaves in a similar way to a mass in a gravitational field.<br />In a gravitational field, an object which moves towards the earth;<br />experiences a force that converts P.E. to K.E.<br />When energy is converted from one form to another;<br />work is done.<br />No work is done in the component that is parallel to the ground.<br />Motion of Charges in a Field<br />
  40. 40. In an electric field, the same applies.<br />When a charge moves parallel to the conducting surface;<br />no work is done.<br />The force only acts radially from the surface;<br />its velocity is unchanged.<br />There cannot be a field inside a conductor no matter its shape.<br />Motion of Charges in a Field<br />
  41. 41. A charged particle that is free to move in a uniform electric field;<br />behaves in a similar way to a,<br />particle in a gravitational field.<br />Acceleration can be found by modifying Newton II.<br />While a charge remains in the electric field;<br />it will continue to accelerate uniformly.<br />Motion of Charged Particles in a Uniform Electric Field<br />
  42. 42. Note:<br />These equations only apply in a uniform field where;<br />the acceleration is constant.<br /> The motion in two dimensions;<br />must use vector techniques.<br />Two other points must also be remembered:<br />Motion of Charged Particles in a Uniform Electric Field<br />
  43. 43. The acceleration of a particle is either;<br />parallel to the lines of force;<br />(+ive charge)<br />or antiparallel (-ive charge).<br />Any motion at an angle to the lines of electric force;<br />will result in a parabolic path.<br />The motion can be divided into its components;<br />which are independent of each other. <br />Motion of Charged Particles in a Uniform Electric Field<br />
  44. 44. Motion of Charged Particles in a Uniform Electric Field<br />Parallel component will undergo acceleration;<br />perpendicular component will not.<br /><br />
  45. 45. Magnetic Fields<br />Section 2 Topic 3<br />
  46. 46. Magnetic fields are produced by moving electric charges;<br />hence by electric currents.<br />In a bar magnet;<br />iron atoms have electrons that spin.<br />Each spinning electron;<br />tiny ‘magnet’.<br />Magnetic Fields<br />
  47. 47. As all the electrons spin in the same direction;<br />there is no cancellation,<br />magnetic field is stable.<br />Field lines can represent magnetic fields;<br />As they did in electric fields.<br />Magnetic Fields<br />
  48. 48. Magnetic Fields<br />
  49. 49. The field is concentric circles centred on the wire;<br />strongest near the wire.<br />This magnetic field is in addition to;<br />electric field produced by the charges.<br />Oersted’s Law<br />
  50. 50. To determine the direction of the magnetic field around a wire;<br />use Oersted’s right hand rule.<br />Oersted’s Law<br />
  51. 51. Grab the wire with your right hand,<br />Thumb in the direction of the conventional current, I;<br />(i.e. +ive to -ive),<br />Field is in the direction of;<br />curl of your fingers.<br />Oersted's Law<br />Oersted’s Law<br />
  52. 52. To increase the strength of the field increasing the current;<br />the wire can be bent into a loop.<br />Current flow through a circular coil<br />Oersted’s Law<br />
  53. 53. To further increase the strength of the field at the centre of the loop;<br />several loops are used instead of the single wire,<br />to form a flat coil.<br />Each loop of current carrying wire contributes;<br />to a stronger magnetic field.<br />Oersted’s Law<br />
  54. 54. Oersted’s Law<br />Current flow through a solenoid<br />
  55. 55. Magnetic Force Around a Current-Carrying Conductor<br />
  56. 56. Magnetic Force Around a Current-Carrying Conductor<br />
  57. 57.  F = BIlsinθ<br />F is the force on the wire,<br />in newtons,<br />I is the current flowing in the wire,<br />in amperes,<br />B is the magnetic induction of the magnetic field,<br />in tesla,<br />lsinθis the length of wire in the magnetic field,<br />in metres.<br />Magnetic Force Around a Current-Carrying Conductor<br />
  58. 58. F = BIlsin<br /> is the angle;<br />between the wire,<br />and the magnetic field.<br />Note sin is at a maximum when;<br /> = 90o,<br />ie when Band I are perpendicular.<br />Magnetic Force Around a Current-Carrying Conductor<br />
  59. 59.  This leads to the definition of B<br />The magnitude B of a magnetic field is defined as the force per current element placed at right angles to the field.<br />The direction of magnetic induction is perpendicular to both the force and the current element.<br />Magnetic Force Around a Current-Carrying Conductor<br />
  60. 60. The principle of a moving coil loudspeaker is that;<br />a coil carrying an electric current,<br />oscillating with amplitude,<br />and frequency,<br />proportional to the sound to be produced,<br />is suspended in a uniform magnetic field.<br />Moving Coil Loudspeaker<br />
  61. 61. Components<br />Cross section of a Speaker<br />
  62. 62. Action of a Loudspeaker<br />
  63. 63. Action of a Loudspeaker<br />
  64. 64. Motion of Particles in Magnetic Fields<br />Section 2<br />Topic 4<br />
  65. 65. Charges that are stationary;<br />have no magnetic force applied to it.<br />A wire that has no P.D. applied to its ends;<br />has no magnetic force associated.<br />We have investigated current carrying conductors;<br />and the magnetic force associated with it.<br />Forces on Moving Charges<br />
  66. 66. Another way to produce an electric current is;<br />to have a moving beam of charged particles.<br />If the beam were to move perpendicularly into a magnetic field;<br />then every charged particle would experience a force.<br />Forces on Moving Charges<br />
  67. 67. It must be perpendicular as from;<br />F = BIl sin , sin  = 0.<br />Force would be zero;<br />if the motion was parallel to the field.<br />If the beam was visible;<br />seen to be deflected by,<br />magnetic interaction.<br />Forces on Moving Charges<br />
  68. 68. The magnitude of the force acting on the beam is determined by:<br />F = BIl<br />Il needs to be determined for a beam of particles;<br /> each of charge q,<br />moving at a constant speed v.<br />The force on the beam is F=IlB=nqvB<br />Thus the force on each particle = qvB<br />Forces on Moving Charges<br />
  69. 69. Substituting into F = BIlsin;<br />F = qvB sin<br />Where  is the angle between v and B.<br />This equation gives the magnitude;<br />direction is determined by the right hand palm rule.<br />Forces on Moving Charges<br />
  70. 70. A beam of charged particles in a magnetic field;<br />can follow a semi-circular path,<br />with uniform circular motion.<br />The radius and other features can easily be determined.<br />The magnetic force,<br />supplies a centripetal force, therefore:<br />Forces on Moving Charges<br />
  71. 71. Forces on Moving Charges<br />FB = Fc<br />and rearranging gives the equation:<br />
  72. 72. This deflection occurs because;<br />the charged particles are no longer constrained by,<br />the lattice of metal ions in the wire.<br /> The deflection of the beam is determined;<br />by the right hand palm rule.<br />Be careful as the thumb must point in the direction of conventional current;<br />i.e. +ive to -ive.<br />Forces on Moving Charges<br />
  73. 73. The period of the motion and the frequency of revolution can be deduced from:<br />Forces on Moving Charges<br />
  74. 74. A cyclotron is a device used;<br />to accelerate charged particles to high energies,<br />generally so they may collide with atomic nuclei,<br />and produce a nuclear reaction.<br />Applications – Cyclotrons<br />
  75. 75. Applications – Cyclotrons<br />
  76. 76. There are three main parts of a cyclotron:<br />1. Ion Source<br />A beam of protons;<br />or sometimes deuteron,<br />which is heavy hydrogen.<br /> Can be charged particle<br />Positive Ion<br />Negative Ion<br />Applications – Cyclotrons<br />
  77. 77. Modern ion sources are generated from an electric arc;<br />external to the cyclotron,<br />vacuum is not compromised.<br />Applications – Cyclotrons<br />
  78. 78. Applications – Cyclotrons<br />
  79. 79. 2. Semicircular Metal Containers (‘dees’)<br />Originally, two hollow copper electrodes;<br />shaped like the letter ‘D’,<br />their straight edges facing each other were used.<br />Applications –Cyclotrons<br />
  80. 80. A large ac P.D. is applied between the dees.<br />The P.D. creates an electric field;<br />in the gap between them,<br />that is continuously changing.<br />As the dees are closed hollow metal conductors;<br />they have no electric field inside of them.<br />Applications –Cyclotrons<br />
  81. 81. The dees are in a magnetic field;<br />produced by an electromagnet.<br />This means that there is a magnetic field;<br />within the dees.<br />Within the gap there exists;<br />an electric and magnetic field.<br />Applications –Cyclotrons<br />
  82. 82. 3. Evacuated Outer Chamber<br />The dees are placed;<br />within an outer evacuated container.<br />Applications –Cyclotrons<br />
  83. 83. The function of the electric field;<br />accelerate the ions to high energies.<br />The longer the ions is in the electric field;<br />the higher the energy.<br />How a Cyclotron Works<br />
  84. 84. The function of the magnetic field;<br />Make the ions move in a circular path;<br />it repeatedly comes under the influence of the electric field,<br />increases the energy level.<br />How a Cyclotron Works<br />
  85. 85. How a Cyclotron Works<br />
  86. 86. How a Cyclotron Works<br />
  87. 87. How a Cyclotron Works<br />
  88. 88. How a Cyclotron Works<br />Cyclotron<br />
  89. 89. As the ions pass through the gap;<br />their speed increases,<br />so must their kinetic energy.<br />This means work is done.<br />From previously;<br />W = qV<br />As there are two passes of the gap per revolution;<br />their kinetic energy per revolution,<br />is 2qV.<br />Energy Transferred to the Ions<br />
  90. 90. The dees are placed between;<br />poles of an electromagnet.<br />The ions are not shielded from;<br />magnetic field,<br />unlike the electric field.<br />This means the ions are affected;<br />inside thedees,<br />in the gap between them.<br />Application- Cyclotrons<br />
  91. 91. To make the ions move in circular path;<br />uniform magnetic field is needed,<br />perpendicular to the plane of the dees.<br />Polarity of the field is important;<br />to make the ions move in the right direction.<br />The force is such that;<br />always acting towards the centre of the circle,<br />causing centripetal acceleration.<br />Application- Cyclotrons<br />
  92. 92. Application- Cyclotrons<br /><ul><li>The field must be in a direction which is;
  93. 93. OUT of the page.</li></li></ul><li>Period of Circular Motion<br />And F = qvB<br />therefore, upon rearrangement:<br />
  94. 94. As the mass m;<br />charge q,<br />magnetic field B,<br />are all constant,<br />rv<br />Period of Circular Motion<br /><br />
  95. 95. We also stated:<br />The time for the ion to complete one semicircle is the same irrespective of the speed of the ion.<br />From before, if the speed doubles;<br />radius doubles.<br />Period of Circular Motion<br />
  96. 96. This also doubles the;<br />circumference (2r).<br />Mathematically, this can also be shown to be true.<br />The velocity of an object undergoing circular motion is given by:<br />Period of Circular Motion<br />
  97. 97. Period of Circular Motion<br />Rearranging for T<br />From  we can substitute for r.<br />
  98. 98. This shows that the period is;<br />independent of speed,<br />or radius.<br />Period of Circular Motion<br /><br />
  99. 99. An alternative method is required.<br />K = ½mv2<br />If we rearrange equation <br />Kinetic Energy of Ions<br />
  100. 100. Substituting into formula for K:<br />Kinetic Energy of Ions<br />
  101. 101. This indicates that the kinetic energy of an ion;<br />of given charge,<br />and mass.<br />Only depends on the radius;<br />of the final circle,<br />magnitude of the magnetic field.<br />This can be understood due to two points.<br />Kinetic Energy of Ions<br />
  102. 102. Point 1<br />If the magnetic field increases;<br />the radii decreases,<br />ions make more revolutions,<br />more crossings of the gap between the dees.<br />Kinetic Energy of Ions<br />
  103. 103. At each crossing;<br />they are accelerated,<br />to higher kinetic energy.<br />Increasing the magnetic field results in;<br />increase of the kinetic energy,<br />of the emerging ions,<br />at a given radius.<br />Kinetic Energy of Ions<br />
  104. 104. Point 2<br />If the P.D. is increased;<br />the ions gain more speed with each crossing of the gap,<br />and so make circles with larger radii,<br />and make fewer revolutions.<br />This means that a larger P.D. does not result in;<br />a larger kinetic energy,<br />of the emerging ions at a given radius.<br />Kinetic Energy of Ions<br />
  105. 105. The protons are used to bombard stable atoms;<br />carbon,<br />nitrogen,<br />oxygen,<br />Fluorine.<br />To produce radioactive forms of these elements.<br />Uses of Cyclotrons in Hospitals<br />
  106. 106. They are then combine with glucose and are given to the patient.<br />The radioactivity can then be detected;<br />bodily functions that use the above chemicals,<br />can be monitored.<br />A medical diagnosis can then be made.<br />Uses of Cyclotrons in Hospitals<br />