Electromagnetism material

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Electromagnetism material

  1. 1. Electricity and Magnetism
  2. 2. Magnetic Effect of a Current In 1819, Hans Christian Oersted accidentally discovered that a compass needle deflected when the current was switched on.
  3. 3. Oersted’s Experiment
  4. 4. A current-carrying conductor produces a magnetic field around it
  5. 5. • Magnetic field pattern around a straight wire. • The resulting magnetic field lines form concentric circles around the wire. The Right-Hand Grip rule can be used to predict the direction of the magnetic field
  6. 6. Magnetic field around a wire carrying current The magnetic field of a long, straight current- carrying wire is stronger: 1) when it is closer to the wire, or 2) when a larger current flows through the wire.
  7. 7. Maxwell’s Equations Relate Electric and Magnetic fields generated by charge and current distributions. 1,,In vacuum 2 0000 cHBED  t D jH t B E B D       0 E = electric field D = electric displacement H = magnetic field B = magnetic flux density = charge density j = current density 0 (permeability of free space) = 4 10-7
  8. 8. Maxwell’s 1st Equation 000 1 Q dVSdEdVEE VSV  0 2 0 3 0 4 4 q r dSq SdE r r q E spheresphere   0 E  8 Equivalent to Gauss’ Flux Theorem: The flux of electric field out of a closed region is proportional to the total electric charge Q enclosed within the surface. A point charge q generates an electric field Area integral gives a measure of the net charge enclosed; divergence of the electric field gives the density of the sources.
  9. 9. Gauss’ law for magnetism: The net magnetic flux out of any closed surface is zero. Surround a magnetic dipole with a closed surface. The magnetic flux directed inward towards the south pole will equal the flux outward from the north pole. If there were a magnetic monopole source, this would Maxwell’s 2nd Equation0B  00 SdBB  Gauss’ law for magnetism is then a statement that There are no magnetic monopoles
  10. 10. Equivalent to Faraday’s Law of Induction: (for a fixed circuit C) The electromotive force round a circuit is proportional to the rate of change of flux of magnetic field, through the circuit. Maxwell’s 3rd Equation t B E   dt d SdB dt d ldE Sd t B SdE C S SS     ldE  SdB  N S Faraday’s Law is the basis for electric generators. It also forms the basis for inductors and transformers.
  11. 11. Maxwell’s 4th Equation jB  0 t E c jB   20 1 ISdjSdBldB C S S 00  Originates from Ampère’s (Circuital) Law : Satisfied by the field for a steady line current (Biot- Savart Law, 1820): r I B r rldI B 2 4 0 3 0 currentlinestraightaFor   Ampère Biot
  12. 12. Magnetic field pattern around a flat coil The magnetic field of a straight wire wound into a flat coil. The magnetic field at the centre of the coil is stronger as the magnetic field lines are closer. There are two ways to increase the magnetic field strength at the centre of the flat coil: 1) Increase the current. 2) Increase the number of turns of the coil.
  13. 13. For loop or coil of wire, can still use 1st RHR, but direction of current constantly changes. Easier to use 2nd Right Hand Rule. Fingers curl in direction of current, thumb points to direction of magnetic field.
  14. 14. Magnetic field of a loop of wire carrying current R I B o 2
  15. 15. Magnetic Field of Multiple Stacked Loops of Current-Carrying Wire • The strength of the field is greater than in a single loop. R IN B o 2 N is the NUMBER of loops
  16. 16. Magnetic Field of a Solenoid nIB centersolenoid 0, A solenoid is a helix, so it behaves differently than stacked loops. The major factor for the magnetic field produced by a solenoid is the turn spacing. n is the turn density, the number of turns per unit length (n = N/L) At the ends of the solenoid, about half the field “leaks out”. nIB endssolenoid 02 1 ,
  17. 17. Magnetic Force • If current exert forces on magnets, then magnets ought to exert forces on currents. • Ampere: – passed current through two parallel wires – one fixed wire and one suspended to swing freely – free wire swung in response to B-field produced by current passing through other wire
  18. 18. Force on a Moving Charge• A charge q moving through a magnetic field (B) with velocity v, experiences a force, FM, proportional to q, v, and B. • Only relative motion is necessary. Charge can be at rest and the magnetic field can be moving relative to the charge. • Direction of the magnetic force is perpendicular to the plane determined by the velocity and B-field vectors. • Magnitude of FM depends on angle between v & B. • When particle moves parallel to the field, the force is zero. When the particle moves perpendicular to the field, the force is a maximum. sinqvBFM
  19. 19. Force on a Moving Charge
  20. 20. 3rd Right Hand Rule Version A • Gives direction of the magnetic force exerted on a conventional current (or positive charge) by an external magnetic field • Point fingers of RH in direction of current (or motion of charge) • Curl fingers through smallest angle to direction of magnetic field • Thumb indicates direction of the force. • If charge or current is negative, direction of force is opposite (or use left hand).
  21. 21. 3rd Right Hand Rule Version B • Point thumb of RH in direction of current (or motion of charge) • Straight fingers point in direction of magnetic field • Palm pushing indicates direction of magnetic force
  22. 22. Magnetic Deflecting Force on a Charged Particle • Because FM is perpendicular to v, it is a deflecting force. • It changes the direction of v, without changing the magnitude. • No work is done on a moving charge by a B-field. • No change in the particle’s energy will occur in the process.
  23. 23. Magnetic Deflecting Force on a Charged Particle • If the field is large enough, the direction of the force on the particle will continuously change, but will always be perpendicular to the charge’s velocity. • The particle will be forced to move in a circular arc (or even a complete circle).
  24. 24. Particles in a Magnetic Field: What is the direction of the particle velocity?
  25. 25. Trajectory of a Free Particle • The particle experiences a centripetal acceleration. • The magnetic deflecting force is therefore a centripetal force. • If v is perpendicular to B, the radius of the charged particle’s trajectory can be easily predicted. qB mv R R mv qvB R mv Fcent 2 2 momentum
  26. 26. Particle Accelerators• In a particle accelerator, the goal is to obtain the largest possible momentum, mv. • This is done by imparting energy to the particle, such as by applying an external E-field. This will increase the momentum of the particle. • Simultaneously increasing the B-field will keep the radius constant. • In a particle accelerator, the largest possible field and radius are required for a given charge. • At Fermilab and CERN, the particle accelerators are 6.3 km and 27 km in circumference, respectively.
  27. 27. Television Screens • Consists of cathode ray tube (CRT) in which electric fields form a beam of electrons. • Phosphor on the TV screen glows when struck by beam. • Pair of coils on the tube neck create a set of perpendicular magnetic fields. • As the electron beam passes through each set of coils, it is deflected either horizontally or vertically to different regions of the screen. • The current through the coils can be varied, thereby varying the magnetic field and the degree of deflection.
  28. 28. Particles in Magnetic Fields • All freely accelerating charges radiate electromagnetic energy (we will discuss this in depth later in the year). • Therefore, a charged particle moving through a magnetic field will lose energy as it experiences a centripetal acceleration. • If it loses kinetic energy, the radius of its trajectory will decrease and it will spiral inward.
  29. 29. Forces on Wires • Consider a quantity of charge q passing through a wire in a B- field, such that in time t, the charges travels a length of wire l. • Direction of the force is the same as the direction of the force on the individual positive charge carriers. Use RHR. sin sin sin sin IlBF BtvtqF t t qvBF qvBF tvl tqI M M M M
  30. 30. Magnetic Force on Current- Carrying Wire
  31. 31. Force on a Current Loop• Imagine a lightweight current-carrying rectangular coil placed in uniform B-field. • Direction and magnitude of the force on each segment of wire depends on the wire’s orientation in the B-field. • Forces may or may not cause the loop to rotate. No rotation when loop is perpendicular to B-field.
  32. 32. Torque on a Current Loop • Suspend the loop so it can rotate freely about a vertical axis and place it in a uniform horizontal B- field. • If the loop is not perpendicular to the field, the forces on the vertical segments of wire produce a torque that rotates the coil through the field. • The torque on the current loop is given by where is the angle between the magnetic dipole moment and B. sinNIAB The DC motor is simple, yet very important application.
  33. 33. Magnetic Dipole Moment• Tendency of a magnet to align with external B-field. • For a planar loop, direction is given by Right-Hand- Current Rule (2nd RHR) • Magnitude is product of current in the loop and area of the loop. • Analyzing the torque on the current loop, it is clear why the magnetic moment tends to align with the external B- field. IAl
  34. 34. Two Parallel Wires • Two long parallel wires suspended next to each other will either attract or repel depending on the direction of the current in each wire. • B-field produced by each wire interacts with current in the other wire • Produces magnetic deflecting force on other wire. • Wires exert equal and opposite forces on each other.
  35. 35. Two Parallel Wires Currents in Same Direction… Wires Attract Currents in Opposite Directions… Wires Repel
  36. 36. Two Parallel Wires • B-field produced by wire 2 at the position of wire 1 is given by where d is the distance between the wires. d I B 2 20 2
  37. 37. Two Parallel Wires • Since the wires are parallel, the force exerted by wire 2 on wire 1 is given by • However, it is often more appropriate to determine the force per unit length on the wire. d II lF d I lIF lBIF M M M 2 2 210 20 1 21 d II BI l FM 2 210 21
  38. 38. Magnetic field pattern around a flat coil A solenoid is obtained by increasing the number of turns of a flat coil. The resulting magnetic field pattern of a solenoid resembles that of a bar magnet.
  39. 39. Magnetic field pattern around a flat coil The magnetic field strength in a solenoid can be increased by: 1) increasing the current, 2) increasing the number of turns per unit length of the solenoid, or 3) placing a soft iron core within the solenoid. The soft iron core concentrates the magnetic field lines, thereby increasing the magnetic field strength.
  40. 40. Uses of Electromagnets 1) Circuit Breaker - A safety device that switches off the electric supply when excessive current flows through the circuit. Uses an electromagnet to open the circuit. Normal condition The basic circuit breaker consists of a simple switch, connected to either a bimetallic strip or an electromagnet. The diagram on the left shows a typical electromagnet design. The hot wire in the circuit connects to the two ends of the switch. When the switch is flipped to the on position, electricity can flow from the bottom terminal, through the electromagnet, up to the moving contact, across to the stationary contact and out to the upper terminal.
  41. 41. Circuit breaker in operation The electricity magnetizes the electromagnet. Increasing current boosts the electromagnet's magnetic force, and decreasing current lowers the magnetism. When the current jumps to unsafe levels, the electromagnet is strong enough to pull down a metal lever connected to the switch linkage. The entire linkage shifts, tilting the moving contact away from the stationary contact to break the circuit. The electricity shuts off.
  42. 42. Uses of Electromagnets 2) Magnetic Relay - A device to control the switch of another circuit without any direct electrical contact between them.
  43. 43. Uses of Electromagnets 3) Electric Bell - The electromagnet forms the core of the electric bell. When the bell button is pressed, the circuit is closed and current flows. The electromagnet becomes magnetised, attracting the soft iron armature and the hammer strikes the gong. However, the circuit will break and the electromagnet loses its magnetism and the springy metal strip pull back the armature and the circuit is closed again. The process repeats.
  44. 44. Uses of Electromagnets 4) Magnetic Resonance Imaging (MRI) - A popular method of medical imaging that provides views of tissues in the body. It is a huge scanner containing a solenoid made of superconductors.
  45. 45. Force on current-carrying conductors - When you placed a current-carrying wire in a magnetic field, the wire experiences a force. This is called the motor effect. - This force acts perpendicular to both the direction of the current and the direction of the magnetic field.
  46. 46. Force on current-carrying conductors A change in the direction of the current in the wire will cause a change in the direction of the force, with the direction of the magnetic field staying constant. Similarly, a change in the direction of the magnetic field will cause a change in the direction of the force, with the direction of the current in the wire staying constant.
  47. 47. Force on charge particles - When you placed a charged particle in a magnetic field, it experiences a force. The direction of deflection for these charged particles can be predicted by Fleming’s left hand rule.
  48. 48. Force on charge particles Magnetic field into page Positively charged particle deflected upwards Negatively charged particle deflected downwards A change in the direction of the magnetic field will cause a change in the deflection of the charged particles, with the direction of the particles staying constant.
  49. 49. Fleming’s Left-Hand Rule We can easily deduce the direction of the force on the current-carrying wire when it is placed in a magnetic field using Fleming’s Left-Hand Rule. It helps us to predict the direction of motion or force.
  50. 50. Why does a current-carrying conductor experience a force when placed in a magnetic field -Magnetic fields that are in the same direction make the combined fields stronger. -Magnetic fields that are in opposite direction make the combined fields weaker.
  51. 51. The force between two parallel wires If we place two current carrying wires held parallel to each other, they always attract or repel each other. The direction of force of attraction is given by the Fleming’s left hand rule. According to the Fleming’s left hand rule, if we stretch our fore finger , middle finger and the thumb of left hand so that they are mutually perpendicular to each other, then the fore finger indicates the direction of produced magnetic field due to the another wire, middle finger indicated the direction of current in the wire and the thumb indicates the direction of force.
  52. 52. The force between two parallel wires Parallel wires carrying currents will exert forces on each other. One wire sets up a magnetic field that influences the other wire, and vice versa. When the current goes the same way in the two wires, the force is attractive. You should be able to confirm this by looking at the magnetic field set up by one current at the location of the other wire, and by applying the right-hand rule.
  53. 53. The force between two parallel wires Parallel wires carrying currents will exert forces on each other. One wire sets up a magnetic field that influences the other wire, and vice versa. When the currents go opposite ways, the force is repulsive. You should be able to confirm this by looking at the magnetic field set up by one current at the location of the other wire, and by applying the right-hand rule.
  54. 54. Force on a current-carrying rectangular coil in a magnetic field The catapult effect shows the force on a wire in a magnetic field when current flows through the wire. It follows then that a wire in a field from a permanent magnet will feel a force when current flows through it. The magnetic field generated around the wire by the current will interact with the field around the magnet and the two fields will push or pull on each other. The magnetic field around a straight wire is circular. The magnetic field between two attracting poles is straight. When the two interact, the wire is pushed away from the field between the attracting poles at right angles (90°) both to the straight field lines and to the direction of current flow.
  55. 55. The D.C. Motor A direct current (DC) motor is a fairly simple electric motor that uses electricity and a magnetic field to produce torque, which turns the motor.
  56. 56. The D.C. Motor A split - ring commutator (sometimes just called a commutator) is a simple and clever device for reversing the current direction through an armature every half turn. The commutator is made from two round pieces of copper (held apart and do not touch each other), one on each side of the spindle. A piece of carbon (graphite) is lightly pushed against the copper to conduct the electricity to the armature. The carbon brushes against the copper when the commutator spins. As the motor rotates, first one piece of copper, then the next connects with the brush every half turn.The wire on the left side of the armature always has current flowing in the same direction, and so the armature will keep turning in the same direction.
  57. 57. Current in this arm flowing from left to right. Current in the same arm reverses, flowing from right to left. Current stops flowing momentarily in the coil but inertia will propel it to make contact once again, reversing the current in the coil.
  58. 58. To increase the turning effect on the wire coil, we can: 1) increase the number of turns on the wire coil. 2) increase the current in the coil. 3) Insert a soft-iron cylinder at the center of the coil of wires.
  59. 59. A.C. motor An AC motor is an electric motor that is driven by an alternating current. It consists of two basic parts, an outside stationary stator having coils supplied with alternating current to produce a rotating magnetic field, and an inside rotor attached to the output shaft that is given a torque by the rotating field.
  60. 60. Similarities & Differences between A.C. / D.C. Motor DC Motor AC Motor Similarities 1. To convert electrical energy to rotational mechanical energy. 1. To convert electrical power to rotational mechanical energy. Differences 1. Commutator present. 2. Cheap. 3. Fixed speed. 4. Requires direct current. 1. Absence of commutator (use slip rings). 2. Expensive. 3. Variable speed. 4. Requires alternating current.

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