12.1

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12.1

  1. 1. Electromagnetism Topic 12.1 Electromagnetic Induction
  2. 2. Induced Electromotive Force (e.m.f.) <ul><li>What is electromagnetic induction? </li></ul><ul><li>The diagram shows a copper rod connected to an ammeter: </li></ul><ul><li>There is no battery in the circuit. </li></ul>
  3. 3. <ul><li>What happens when you move the copper rod downwards, to cut across the horizontal magnetic field? </li></ul><ul><li>The pointer on the meter makes a brief `flick' to the right, showing that an electric current has been induced. </li></ul>
  4. 4. <ul><li>What happens when you move the rod upwards? </li></ul><ul><li>The meter again gives a `flick', but this time to the left. </li></ul><ul><li>You have now induced a current in the opposite direction. </li></ul>
  5. 5. <ul><li>If you hold the rod stationary, or if you move the rod along the field lines, there is no induced current. </li></ul>
  6. 6. Why does electromagnetic induction occur? <ul><li>When you move the copper rod, its free electrons move with it. </li></ul><ul><li>But when a charge moves in a magnetic field it experiences a force on it </li></ul><ul><li>(the B Q v force). </li></ul><ul><li>You can use Flemings Left hand Rule to show that the force on each electron is to the left as shown in the diagram </li></ul><ul><li>(Remember that an electron moving down has to be treated like a positive charge moving up. </li></ul>
  7. 8. <ul><li>So electrons accumulate at one end of the rod, making it negative. </li></ul><ul><li>This leaves the other end short of electrons and therefore positive. </li></ul><ul><li>There is now a voltage (potential difference) across the ends of the moving rod. </li></ul><ul><li>If the ends of the moving rod are joined to form a complete circuit, the induced voltage causes a current to flow round the circuit as shown by the flick of the ammeter. </li></ul>
  8. 9. <ul><li>The induced voltage is a source of electrical energy ‑ an e.m.f </li></ul><ul><li>When a conductor is moving in a magnetic field like this, an e.m.f is induced, even if there isn't a complete circuit for a current to flow. </li></ul>
  9. 10. Formula for a Straight Conductor <ul><li>Consider a conductor of length l that moves with velocity v perpendicular to a magnetic flux density or induction B as shown in the figure. </li></ul>
  10. 11. <ul><li>When the wire conductor moves in the magnetic field, the free electrons experience a force because they are caused to move with velocity v as the conductor moves in the field. </li></ul><ul><li>F = e v B </li></ul>
  11. 12. <ul><li>This force causes the electrons to drift from one end of the conductor to the other, and one end builds‑up an excess of electrons and the other a deficiency of electrons. </li></ul><ul><li>This means that there is a potential difference or emf between the ends. </li></ul><ul><li>Eventually, the emf becomes large enough to balance the magnetic force and thus stop electrons from moving. </li></ul>
  12. 13. <ul><li>evB = eE ( from F = evB and F = eE) </li></ul><ul><li>Therefore E = Bv </li></ul><ul><li>If the potential difference (emf) between the ends of the conductor is ε then </li></ul><ul><li>ε = E L (from E = V/d) </li></ul><ul><li>By substitution we have </li></ul><ul><li>ε = B v L </li></ul>
  13. 14. Magnetic Flux <ul><li>The magnetic flux ( Φ ) through a region is a measure of the number of lines of magnetic force passing through that region. </li></ul><ul><li>Φ = AB cos θ </li></ul><ul><li>where A is the area of the region and θ is the angle of movement between the magnetic field and a line drawn perpendicular to the area swept out. </li></ul><ul><li>The unit of magnetic flux is the weber Wb. </li></ul>
  14. 15. <ul><li>For a single conductor in the magnetic flux density, it can be seen that </li></ul><ul><li>ε = - ΔΦ / Δ t (the rate of change of flux density) </li></ul><ul><li>For N number of conductors as in the case for a solenoid, the term flux‑linkage is used. </li></ul><ul><li>Then </li></ul><ul><li>ε = - N Δ ( Φ / Δ t) </li></ul><ul><li>This is Faraday’s Law </li></ul><ul><li>The minus sign shows us that the emf is always produced so as to oppose the change in flux. </li></ul>
  15. 16. Time-changing Magnetic Flux <ul><li>Therefore the production of an emf is produced by a time changing magnetic flux. </li></ul><ul><li>This could be due to the wire or coil moving through a magnetic field </li></ul><ul><li>Or by an increasing or decreasing magnetic field of an electromagnet next to a wire or coil. </li></ul>
  16. 17. Faraday’s Law <ul><li>We know that an e.m.f. is induced when there is a change in the flux linking a conductor. </li></ul><ul><li>Faraday's law makes the connection between the size of the induced e.m.f. and the rate at which the flux is changing. </li></ul><ul><li>It states that: </li></ul><ul><li>the magnitude of the induced e.m.f is directly proportinonal to the rate of change of magnetic flux or flux linkage. </li></ul>
  17. 18. Linking <ul><li>For a single conductor in the magnetic flux density, it can be seen that </li></ul><ul><li>ε = - ΔΦ / Δ t (the rate of change of flux density) </li></ul><ul><li>And ε = B v l </li></ul><ul><li>Therefore - ΔΦ / Δ t = B v l </li></ul>
  18. 19. Lenz’s Law <ul><li>Faraday's law tells us the size of the induced e.m.f., but we can find its direction using Lenz's law </li></ul><ul><li>The direction of the induced e.m.f is such that it will try to oppose the change in flux that is producing it. </li></ul>
  19. 21. <ul><li>Lenz's law is illustrated in the diagrams: As you move the N‑pole into the coil, an e.m.f. is induced which drives a current round the circuit as shown. </li></ul><ul><li>Now use the right‑hand grip rule </li></ul><ul><li>Can you see that the current produces a magnetic field with a N‑pole at the end of the coil nearest to the magnet? </li></ul><ul><li>So the coil repels the incoming magnet, and in this way the induced current opposes the change in flux. </li></ul>
  20. 22. <ul><li>Why is the current reversed as you move the N‑pole out? </li></ul><ul><li>By Lenz's law, the coil needs to attract the receding N‑pole </li></ul>
  21. 23. <ul><li>Lenz's law is a result of the conservation of energy. If you move the magnet into the coil, you feel the repulsive force. </li></ul><ul><li>You have to do work to move the magnet against this force. </li></ul><ul><li>And so energy is transferred from you (or the system that is moving the magnet) to the electrical energy of the current. </li></ul>
  22. 27. <ul><li>Interactive Faraday </li></ul><ul><li>Emf </li></ul><ul><li>Faraday </li></ul>

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