Lecture 5 Section 7


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Lecture 5 Section 7

  1. 1. Chapter 5 Electricity and Magnetism
  2. 2. Outline <ul><li>Charge </li></ul><ul><ul><li>Defining charge </li></ul></ul><ul><ul><li>Forces on charges: Coulomb’s law </li></ul></ul><ul><li>Electricity and matter </li></ul><ul><li>Current </li></ul><ul><ul><li>Potential difference </li></ul></ul><ul><ul><li>Ohm’s Law </li></ul></ul><ul><ul><li>Electric power </li></ul></ul><ul><li>Magnetism </li></ul><ul><ul><li>Magnetic forces </li></ul></ul><ul><ul><li>Magnetic field </li></ul></ul><ul><ul><li>The connection between electricity and magnetic fields </li></ul></ul><ul><li>Applications </li></ul>
  3. 3. Charge <ul><li>We have been discussing a basic property of matter called mass </li></ul><ul><li>In electricity, the basic concept is called charge </li></ul><ul><li>Classical mechanics doesn’t explain what mass is, just how it behaves: how it moves, etc. </li></ul><ul><li>Similarly, classical E & M (electricity and magnetism) does not tell us what charge is exactly, only how it behaves </li></ul>
  4. 4. Positive and Negative Charges <ul><li>Ben Franklin (1706-1790) named the two kinds of charges: Positive and Negative </li></ul><ul><li>All charge is either positive or negative </li></ul><ul><li>Like charges repel each other </li></ul><ul><li>or </li></ul><ul><li>Opposite charges attract each other </li></ul>- - + + - +
  5. 5. Net Charge <ul><li>Net Charge: the total amount of charge on an object </li></ul><ul><ul><li>For most objects the net charge = zero </li></ul></ul><ul><li>“ Charged” means </li></ul><ul><ul><li>Having more of one kind of charge ( + or - ) </li></ul></ul><ul><ul><li>Moving around electrons </li></ul></ul><ul><li>Charges (i.e., electrons) can be moved around </li></ul><ul><ul><li>By friction </li></ul></ul><ul><ul><li>By induction </li></ul></ul>
  6. 6. Friction and Induction <ul><li>Friction </li></ul><ul><ul><li>Charges from one object are transferred to another </li></ul></ul><ul><li>Induction </li></ul><ul><ul><li>A charged object induces a charge separation in a second object </li></ul></ul>
  7. 7. Conservation of Charge <ul><li>The net charge in an isolated system can not change </li></ul><ul><ul><li>This means that the sum of the negative and positive charges in any system remains constant </li></ul></ul><ul><li>One can move charges around, but cannot create or destroy charge </li></ul>
  8. 8. Defining Charge <ul><li>All matter is composed of atoms </li></ul><ul><li>All atoms are composed of three elementary particles </li></ul><ul><ul><li>Protons (mass = 1.673 x 10 -27 kg, charge = 1.06 x 10 -19 Coulombs) </li></ul></ul><ul><ul><li>Electrons (mass = 9.11 x 10 -31 kg, charge = -1.06 x 10 -19 Coulombs) </li></ul></ul><ul><ul><li>Neutron s (mass = 1.675 x 10 -27 kg, charge = 0 Coulombs) </li></ul></ul><ul><li>1 Coulomb = 6.25 × 10 18 electrons </li></ul>
  9. 9. Coulomb’s Law <ul><li>Force between two point charges </li></ul><ul><ul><li>The force exerted by one charged object on another charged object is proportional to the charge of each object and to the inverse of the (distance) 2 between the objects </li></ul></ul><ul><ul><li>the force can be </li></ul></ul><ul><ul><ul><li>Attractive - oppositely charged objects </li></ul></ul></ul><ul><ul><ul><li>Repulsive - similarly charges objects </li></ul></ul></ul><ul><ul><li>“ k” is called “coulomb’s constant”, (k = 9x10 9 Nm 2 /C 2 ) </li></ul></ul>
  10. 10. Another Inverse Square Law <ul><li>Remember we have already seen the inverse square distance dependence in the universal law of gravity </li></ul><ul><li>In many ways, the force of electrostatic interaction is very similar to the force of gravitational interaction, but there are some major differences </li></ul>
  11. 11. Electrostatic Interactions <ul><li>The force due to electrostatic interaction is much larger than the force due to gravity </li></ul><ul><ul><li>The ratio of the electric and gravitational forces between the electron and proton in a hydrogen atom is F elec /F grav = 2.2 ×10 39 </li></ul></ul><ul><li>So why don’t we notice electrical forces more? </li></ul><ul><ul><li>Masses can not cancel each other while charges can (1 g + 1 g = 2 g, 1 C + -1 C = 0 C) </li></ul></ul><ul><li>The force due to gravity can only be attractive </li></ul><ul><li>Electrostatic forces can be repulsive or attractive </li></ul>
  12. 12. Material Matters <ul><li>For some materials, once an imbalance of charge is produced, the charge “sticks around” </li></ul><ul><ul><li>These materials are called electrical insulators </li></ul></ul><ul><li>For other materials, the charge imbalance is very difficult to achieve---it seems as thought the charge just passes through the material (e.g. metals) </li></ul><ul><ul><li>These materials are called electrical conductors </li></ul></ul>
  13. 13. Levels of Conductivity <ul><li>Conductor </li></ul><ul><ul><li>Material through which electrons can easily move </li></ul></ul><ul><li>Insulator </li></ul><ul><ul><li>Material in which electrons remain fixed in one location under normal circumstances </li></ul></ul><ul><li>But not all materials can be distinctly characterized by these simple definitions </li></ul><ul><ul><li>Semiconductors – Have conductivity between conductor and insulator - used in transistors </li></ul></ul><ul><ul><li>Superconductors – Electrons flow through these materials with no resistance </li></ul></ul>
  14. 14. Ions <ul><li>The conduction of electricity through liquids and gases involves the movement of ions </li></ul><ul><li>Whenever an atom gains or loses an electron, we say that the atom is ionized </li></ul><ul><li>An ion is simply an atom with excess charge </li></ul><ul><ul><li>The ion can be positive or negative </li></ul></ul><ul><li>Ionization can be accomplished in several ways </li></ul><ul><ul><li>Sparks </li></ul></ul><ul><ul><li>Flame </li></ul></ul><ul><ul><li>UV and X-rays </li></ul></ul>
  15. 15. Electric Potential <ul><li>Whenever a potential difference exists, any charge will move to the position with the lowest potential </li></ul><ul><li>Differences in potential are caused by differences in the net value of electric field that varies from point to point in space </li></ul>
  16. 16. Electric Potential <ul><li>Unit: Volt = Joule / Coulomb </li></ul><ul><li>= kg m 2 /s 2  C </li></ul>
  17. 17. Voltage of Batteries <ul><li>Just as every liter of water can do 8 times more work if dropped from 8 times as high, every Coulomb does 8 times more work if the voltage is 8 times as great </li></ul><ul><li>The 12V battery will push 8 times more electrons through the same circuit in a given time. </li></ul>12m 1.5m 12V 1.5V
  18. 18. Electric Current <ul><li>When charge flows from one place to another, an electric current is formed </li></ul><ul><li>Most practical applications of electrical phenomena are based on the understanding of electric current </li></ul><ul><li>Unit of current: Ampere = Coulomb per second </li></ul><ul><li>Some rules for the flow of charge: </li></ul><ul><ul><li>Current can only exist between two points of different potential connected by a conductor </li></ul></ul><ul><ul><li>Current can only exist whenever a conductive path with no breaks is provided </li></ul></ul>
  19. 19. AC/DC <ul><li>AC: Alternating Current (wall socket) </li></ul><ul><li>DC: Direct Current (battery) </li></ul><ul><li>What’s the difference? </li></ul><ul><ul><li>AC: time dependent voltage </li></ul></ul><ul><ul><li>DC: constant voltage </li></ul></ul>
  20. 20. Current: “Flowing” Charge <ul><li>Flow of charge is similar to flowing water </li></ul><ul><ul><li>If the faucet is closed, the flow stops </li></ul></ul><ul><ul><li>If the pump is turned off, the flow stops </li></ul></ul>PUMP FAUCET HOSE OR FILTER
  21. 21. Electric Circuit Elements <ul><li>Battery: source of potential difference </li></ul><ul><li>Resistor: the resistance in an electric circuit is a measure of how “difficult” is is to move charge through the circuit </li></ul>SWITCH (like the faucet) RESISTOR (like crimps in the hose) BATTERY (like the pump)
  22. 22. Ohm’s Law <ul><li>There is a relationship between the current, voltage, and resistance in an electric circuit </li></ul><ul><li>These parameters are usually represented by the letters: </li></ul><ul><ul><li>I  current </li></ul></ul><ul><ul><li>V  voltage </li></ul></ul><ul><ul><li>R  resistance (unit = ohm, symbol =  ) </li></ul></ul><ul><li>They are related by Ohm’s law: </li></ul><ul><ul><li>V = I × R </li></ul></ul>
  23. 23. Electric Shock <ul><li>Electric shock is governed by Ohm’s law </li></ul><ul><ul><li>Lowered resistance means higher current </li></ul></ul><ul><ul><li>High current is deadly! </li></ul></ul><ul><li>A “high voltage” does not directly harm you </li></ul><ul><li>Current is what passes through objects when charges flow toward a lower potential </li></ul><ul><li>According to Ohm’s law: </li></ul><ul><ul><li>Low resistance with high voltage means large current </li></ul></ul>
  24. 24. Electric Shock <ul><li>Typical Resistance of the Human Skin </li></ul><ul><ul><li>Dry: as much as 500,000 Ohms (500k) </li></ul></ul><ul><ul><li>Wet: as little as 100 Ohms (if wet with salt water) </li></ul></ul><ul><li>Currents in the human body 0.001 Amp - you feel it 0.005 Amp - you feel pain 0.010 Amp - muscle spasm with the pain 0.015 Amp - loss of muscle control 0.070 Amp - serious injury </li></ul><ul><li>A current of only 0.070 (or 70 milli-Amps) passing through the heart muscle for more than one second can cause the heart to stop beating </li></ul>
  25. 25. Electric Shock <ul><li>If your skin is dry, then R  500,000  </li></ul><ul><li>Since V = 120 V for most outlets in the US, Ohm’s Law predicts: </li></ul><ul><li>I = V/R = 120 V  500,000  </li></ul><ul><li>= 0.0002 Amps </li></ul><ul><li>Painful, but not deadly </li></ul>
  26. 26. Electric Shock <ul><li>If your skin is wet, then R can be as low as 1,000  </li></ul><ul><li>So for a V = 120 V outlet, we have: </li></ul><ul><li>I = V/R = 120 V  1,000  </li></ul><ul><li>= 0.12 Amps </li></ul><ul><li>Which can be fatal if the current passes through the heart </li></ul>
  27. 27. Electric Power <ul><li>The flow of current is the source of electric energy </li></ul><ul><ul><li>Whenever a current flows, some energy is being transformed into heat </li></ul></ul><ul><ul><li>The remainder of the energy can be used to do work </li></ul></ul><ul><li>The rate at which electric current is doing work is called electric power </li></ul><ul><li>Electric power is proportional to both the current and the potential difference: </li></ul>
  28. 28. Electric Circuits <ul><li>The amount of current flowing through the circuit paths and the effective resistance of the circuit depends upon how the circuit elements are arranged </li></ul><ul><li>Most circuits are arranged in two basic ways: </li></ul><ul><ul><li>Series (voltage split among elements) </li></ul></ul><ul><ul><li>Parallel (current split among elements) </li></ul></ul><ul><li>The amount of current that can flow in a circuit depends on the arrangement of the resistances in the circuit </li></ul>
  29. 29. Series Circuits <ul><li>Series (voltage split among elements) </li></ul><ul><li>Resistance is higher than for a single bulb, so current through the circuit is reduced </li></ul>
  30. 30. Parallel Circuits <ul><li>Current split among elements </li></ul><ul><li>Because the elements in a parallel circuit have the same voltage across them, the current through each bulb is greater than in the series case </li></ul>
  31. 31. Magnetism <ul><li>At one point, electricity and magnetism were understood to be completely separate in nature </li></ul><ul><li>Scientists discovered in the nineteenth century that electrical and magnetic phenomena are actually closely related </li></ul><ul><li>All magnets have two poles, north and south </li></ul><ul><ul><li>Like poles repel </li></ul></ul><ul><ul><li>Opposite poles attract </li></ul></ul>
  32. 32. Electric and Magnetic Forces <ul><li>Both electric and magnetic forces can have an effect on objects without being in direct contact with the objects (Similar to the effect of gravity) </li></ul><ul><li>We explain this ability to do work ‘at a distance’ with the concept of “force fields” </li></ul><ul><li>Anything with mass fills all space with a gravitational field </li></ul><ul><ul><li>It is the field that causes the forces on any mass that lies in the field </li></ul></ul><ul><li>Similarly, every charged particle fills all space with an electric field </li></ul><ul><ul><li>Whenever another charge lies in the electric field, electric forces act on it </li></ul></ul>
  33. 33. The Connection between Electricity and Magnetism <ul><li>Oersted showed that electricity and magnetism were inseparable phenomena </li></ul><ul><li>He showed that a compass could be used to detect the presence of a magnetic field </li></ul><ul><li>Oersted held a compass near a wire through which he passed a current, and found that the compass needle was deflected by the current in the wire </li></ul>
  34. 34. Direction of the Magnetic Field <ul><li>A simple rule, called the right hand rule determines the direction of the magnetic field produced by a wire </li></ul>
  35. 35. The Current Loop Magnet <ul><li>Soon scientists understood that current loop could be considered as a simple magnet </li></ul>
  36. 36. Major Discovery - Induction <ul><li>All moving electric charges produce magnetic fields </li></ul><ul><li>Important Application: </li></ul><ul><ul><li>By using a coil of wire and high current, strong magnetic field can be produced. This is called an electromagnet </li></ul></ul>
  37. 37. Magnetism <ul><li>All magnetic phenomena is produced by moving charges </li></ul><ul><li>Currents are moving charges </li></ul><ul><ul><li>So a magnet exerts force on a current-carrying wire </li></ul></ul><ul><ul><li>And the current carrying wire produces a magnetic field </li></ul></ul><ul><li>Inside materials (e.g. – permanent magnets) </li></ul><ul><ul><li>The moving charge is in the form of electrons spinning around nucleus </li></ul></ul>
  38. 38. The Electric Motor <ul><li>Makes use of the force on a current carrying wire by a magnetic field </li></ul><ul><li>Important component: Commutator </li></ul><ul><ul><li>The commutator changes the direction of the current in the loop so that the force continues to push in the same direction </li></ul></ul>
  39. 39. Generators <ul><li>The basic idea: whenever there is relative motion between a wire loop and a magnetic field, a current is produced </li></ul><ul><li>This is called induced current </li></ul><ul><li>When the direction of the current is changed, the current is called an alternating current </li></ul>
  40. 40. Transformers <ul><li>The idea of induced current led to the development of transformers </li></ul><ul><ul><li>When current is alternating in a loop of wire (called the primary loop), a secondary current can be induced in a nearby loop of wire (the secondary loop) </li></ul></ul><ul><li>Transformers are very useful, since the voltage of the secondary induced current can be controlled by the number of turns </li></ul><ul><ul><li>This is the way electric energy (at about 120 Volts) is delivered to your home from high voltage power lines </li></ul></ul>
  41. 41. Transformer Math <ul><li>The relationship between the voltages in the loops of a transformer is given by </li></ul><ul><li>Large transformers can decrease the voltage by several thousand times </li></ul>
  42. 42. Applications of Magnetism <ul><li>Magnetic Recording </li></ul><ul><ul><li>Video tapes </li></ul></ul><ul><ul><li>Audio tapes </li></ul></ul><ul><ul><li>Computer hard drives </li></ul></ul><ul><li>CRT Television screens </li></ul><ul><ul><li>Use magnets to direct the electrons that provide the source of energy that makes the light you view </li></ul></ul><ul><li>Navigation </li></ul><ul><ul><li>Compasses – man made and biological! </li></ul></ul>
  43. 43. The Compass <ul><li>The earth is a giant magnet </li></ul><ul><li>Useful for navigation </li></ul><ul><ul><li>Compasses </li></ul></ul><ul><ul><li>Birds </li></ul></ul><ul><ul><li>Bacteria </li></ul></ul><ul><ul><li>Cows! </li></ul></ul><ul><ul><li>Humans? </li></ul></ul>
  44. 44. Application of Electrostatics <ul><li>Charging </li></ul><ul><ul><li>The surface of a cylindrical drum is electrostatically charged </li></ul></ul><ul><li>Exposure </li></ul><ul><ul><li>Document is illuminated, bright areas reflect light which create charge conduits in the photoconductor </li></ul></ul><ul><li>Developing </li></ul><ul><ul><li>Positively charged toner sticks to negatively charged areas </li></ul></ul><ul><li>Transfer </li></ul><ul><ul><li>The toner on the drum is transferred to a piece of paper with a higher negative charge </li></ul></ul><ul><li>Fusing </li></ul><ul><ul><li>Toner is melted and bonded to the paper </li></ul></ul><ul><li>Cleaning </li></ul>
  45. 45. E&M Summary <ul><li>Charge is a fundamental property of elementary particles </li></ul><ul><ul><li>Two types: negative and positive </li></ul></ul><ul><ul><li>Unit: Coulomb (C) </li></ul></ul><ul><ul><li>Fundamental charge: 1.06  10 -19 C, called “ e ” </li></ul></ul><ul><li>Atoms are composed of electrons, protons and neutrons </li></ul><ul><ul><li>Electrons have –e , protons have +e, neutrons are neutral </li></ul></ul><ul><ul><li>An atom with a deficit of electrons is a positive ion </li></ul></ul><ul><li>Current is the flow of charge </li></ul><ul><ul><li>Charge flows through a conductor, not through an insulator </li></ul></ul>
  46. 46. E&M Summary <ul><li>Voltage is the term given to the potential difference between two points </li></ul><ul><ul><li>Voltage Unit: Volt (V) </li></ul></ul><ul><li>Relationship between current and voltage: Ohm’s Law: </li></ul><ul><li>V = IR (R is resistance) </li></ul><ul><li>Power: rate of doing work; P=IV </li></ul><ul><li>Permanent magnets when the magnetic field can be lined up </li></ul><ul><li>Electromagnetic induction </li></ul><ul><ul><li>Current produced when there is relative motion between a current loop and a magnetic field </li></ul></ul><ul><ul><li>Basis for the transformer </li></ul></ul>