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• Newton developed a &amp;quot;thought experiment&amp;quot; to demonstrate this concept. Imagine placing a cannon at the top of a very tall mountain. Once fired, a cannonball falls to the Earth. The greater the speed, the farther it will travel before landing. If fired with the proper speed, the cannonball would achieve a state of continuous free-fall which we call orbit. The same principle applies to the Space Shuttle or Space Station. While objects inside them appear to be floating and motionless, they are actually traveling at the same orbital speed as their spacecraft: 17,500 miles per hour (28,000 km per hour)! Objects in a state of free-fall or orbit are said to be &amp;quot;weightless.&amp;quot; The object&apos;s mass is the same, but it would register &amp;quot;0&amp;quot; on a scale. Weight varies depending on if you are on the Earth, the Moon, or in orbit. But your mass stays the same, unless you go on a diet!
• NASA has a Reduced Gravity Aircraft based at the Lyndon B. Johnson Space Centre. It is an airplane called the “Vomit Comet” that flies in a parabolic arc that is approximately 10 kilometres long. The airplane first climbs in altitude and then falls in such a way that the flight path corresponds to that of an object in free fall. The people inside are temporarily weightless for a time period of 25 seconds. Typically one flight lasts two hours in which 40 parabolas are flown.
• NASA has a Reduced Gravity Aircraft based at the Lyndon B. Johnson Space Centre. It is an airplane called the “Vomit Comet” that flies in a parabolic arc that is approximately 10 kilometres long. The airplane first climbs in altitude and then falls in such a way that the flight path corresponds to that of an object in free fall. The people inside are temporarily weightless for a time period of 25 seconds. Typically one flight lasts two hours in which 40 parabolas are flown.
• Fields

1. 1. Physics 40S Unit 2 - Fields
2. 2. Kepler’s Laws <ul><li>Johannes Kepler (1571-1630) was born in southwest Germany. He had been greatly influenced by the work of the Greeks and spent a great deal of time trying to devise systems with which to explain the motion of the planets about the sun. </li></ul>Topic 2.1 – Exploration of Space
3. 3. Kepler’s Laws Topic 2.1 – Exploration of Space
4. 4. Kepler’s 1 st Law <ul><li>Using Tycho's observations of the planet Mars, Kepler found that its motion fitted an elliptical orbit with a high degree of accuracy. He later found that the orbits of the other known planets could be drawn as ellipses, with the sun at one of the foci. </li></ul><ul><li>The motion of the planets in ellipses became known as Kepler's First Law. </li></ul>Topic 2.1 – Exploration of Space
5. 5. Kepler’s 1 st Law <ul><li>An exaggerated diagram of an ellipse and two foci is shown below. The sun is at one of the foci, F 1 . </li></ul>Topic 2.1 – Exploration of Space
6. 6. Kepler’s 1 st Law <ul><li>An ellipse can be defined as a closed curve such that the sum of the distances from any point P on the curve to two fixed points (called the foci F 1 and F 2 ) remains constant. That is, the sum of the distances F 1 P + F 2 P is the same for all points on the curve. A circle is a special case of an ellipse in which the two foci coincide at the centre of the circle. </li></ul><ul><li>We can state Kepler's First Law as follows. </li></ul><ul><li>The planets move about the sun in elliptical orbits, with the sun at one focus of the ellipses. </li></ul>Topic 2.1 – Exploration of Space
7. 7. Kepler’s 2 nd Law <ul><li>Kepler's Second Law further describes the motion of a planet around the sun. This law examined the areas swept out by the planets as they moved around the sun. </li></ul><ul><li>The diagram shows two equal time intervals Δ t 1,2 and Δ t 3,4 . For these time intervals, the areas swept out by the line joining the sun and the planet are equal, that is area A = area B. This means that the closer a planet is to the sun, the faster it will move, and it will move in a predictable way. </li></ul>Topic 2.1 – Exploration of Space
8. 8. Kepler’s 2 nd Law <ul><li>Kepler's ellipses put an end to Greek astronomy. The long established concept of celestial spheres and perfectly circular motion had been destroyed. Kepler's scheme of the solar system has been followed by astronomers and scientists ever since, without significant change. </li></ul><ul><li>Kepler's Second Law can be stated as follows. </li></ul><ul><li>The straight line joining the sun and a given planet sweeps out equal areas in equal intervals of time . </li></ul>Topic 2.1 – Exploration of Space
9. 9. Kepler’s 3 rd Law <ul><li>In 1619, Kepler published a second book. It contained what is now known as Kepler's Third Law . It stated that the square of the orbital period of a planet is proportional to the cube of its mean distance from the sun. It can be expressed mathematically as </li></ul><ul><li>where R is the mean radius of the orbit of the planet, T is the period of revolution about the sun, and K is a constant, usually referred to as Kepler's constant. </li></ul>Topic 2.1 – Exploration of Space
10. 10. Kepler’s 3 rd Law <ul><li>Kepler's constant is K  = 3.35 x 10 18  m 3 /s 2 . By using Kepler's Third Law, it is possible to determine the period of revolution, or the mean radius of orbit for any object in orbit around the sun. </li></ul><ul><li>Kepler's constant can also be determined for objects in orbit around other central bodies. So for example, the motion of the moon around Earth could be used to determine K for our earth. Once we know what the value of K is, then we can also determine the period of revolution or the mean radius of orbit for that object. </li></ul>Topic 2.1 – Exploration of Space Kepler’s Law Experiment
11. 11. Universal Law of Gravitation <ul><li>Newton graduated from Cambridge University in 1665 after majoring in mathematics. In the few years after this, Newton did some of his best thinking. Legend has it that while watching an apple fall, Newton began to wonder if the force that accelerated the fall of the apple might also be the one responsible for maintaining the path of the moon's orbit. The moon is moving around Earth in a circular orbit and thus has centripetal acceleration. This acceleration is caused by the gravitational pull between the moon and Earth. The amount of this acceleration due to gravity was proportional to the gravitational force between Earth and the moon. By using his knowledge of circular motion and Kepler's Third Law, Newton deduced that the gravitational force was inversely proportional to the square of the distance from Earth to the moon. </li></ul>Topic 2.1 – Exploration of Space
12. 12. Universal Law of Gravitation Topic 2.1 – Exploration of Space
13. 13. Universal Law of Gravitation <ul><li>Newton's reasoning was similar to the following. From our work on circular motion, we know that the centripetal force required to keep an object moving in a circle is </li></ul><ul><li>From Kepler's Law and </li></ul>Topic 2.1 – Exploration of Space
14. 14. Universal Law of Gravitation <ul><li>By substituting this value for T 2 into the equation for force, we obtain </li></ul><ul><li>Since the expression (4π 2 K ) is a constant, the force of gravitational attraction on a planet is directly proportional to the mass of the planet and inversely proportional to the square of its distance from the sun . </li></ul>Topic 2.1 – Exploration of Space
15. 15. Universal Law of Gravitation <ul><li>We saw in the previous lesson that Kepler's constant is the same for any object circling the sun, but it would have a different and smaller value for a satellite of Earth. Newton reasoned that this is because the mass of Earth is smaller than the mass of the sun. In other words, Kepler's constant is proportional to the mass of the object exerting the force of attraction at the centre of the orbit. So the expression 4π 2 K is proportional to m c where m c refers to the mass of the central body (like the sun or Earth). </li></ul>Topic 2.1 – Exploration of Space
16. 16. Universal Law of Gravitation <ul><li>We can thus rewrite this expression as 4π 2 K = Gm c . The value G is referred to as a universal gravitational constant. Henry Cavendish first experimentally measured it in 1798. Newton's remarkable extension was to say that if this equation for force applies to the sun and its planets, and to Earth and its moon, then it should apply to any body in the universe that has mass. We can thus summarize Newton's Law of Universal Gravitation as </li></ul><ul><li>Any two bodies attract each other with forces proportional to the mass of each and inversely proportional to the square of the distance between them. </li></ul><ul><li> where G is the Universal Gravitational Constant: G = 6.67 x 10 -11  N·m 2 /kg 2 </li></ul>Topic 2.1 – Exploration of Space
17. 17. Gravitational Potential Energy <ul><li>How do you calculate the gravitational potential energy between 2 masses? </li></ul><ul><li>What is a potential well? </li></ul><ul><li>What is the escape velocity? How is it calculated? </li></ul><ul><li>What is binding energy? How does the binding energy compare in magnitude to the PE g ? </li></ul>Topic 2.1 – Exploration of Space
18. 18. Gravitational Potential Energy <ul><li>How do you calculate the gravitational potential energy between 2 masses? </li></ul><ul><li>To increase the separation of the two masses from R 1 to R 2 requires work to be done to overcome the force of attraction, similar to stretching a spring. When this work is done, the gravitational potential energy increases. To derive a mathematical equation for gravitational potential energy, we need to remember the relationship between gravitational force and separation. </li></ul>Topic 2.1 – Exploration of Space
19. 19. Gravitational Potential Energy <ul><li>A force versus separation graph </li></ul><ul><ul><li>for this situation is like the one shown. </li></ul></ul><ul><li>From our work on work and energy, we learned that the work done by a varying force is simply the area under a force-displacement graph for the interval. To find the area under an inverse square curve requires doing an integration using calculus. </li></ul>Topic 2.1 – Exploration of Space
20. 20. Gravitational Potential Energy <ul><li>The resulting change in </li></ul><ul><ul><li>potential energy is </li></ul></ul><ul><li>When written in this way, the first term in the expression depends on R 2 and the second term on R 1 . Thus, each term is an expression for the gravitational potential energy at that separation. Therefore, at any separation distance R , the gravitational potential energy, PE g , between two masses M 1 and M 2 is given by </li></ul>Topic 2.1 – Exploration of Space
21. 21. Gravitational Potential Energy <ul><li>What is a potential well? </li></ul><ul><li>The equation always produces a negative value. As R increases, that is, as the masses get farther apart, PE g increases by becoming less negative. As R increases to the point of approaching infinity, R -> ∞, the potential energy approaches zero, PE g ->0. In other words, the zero value of gravitational potential energy between two masses occurs when they are infinitely apart. </li></ul>Topic 2.1 – Exploration of Space
22. 22. Gravitational Potential Energy <ul><li>What is a potential well? </li></ul>Topic 2.1 – Exploration of Space
23. 23. Gravitational Potential Energy <ul><li>This type of potential energy relationship, where two objects have a force of attraction between them, resulting in their potential energy being negative, is called a potential well . </li></ul><ul><li>An object must rise out of the potential well to be free of the gravitational force. </li></ul>Topic 2.1 – Exploration of Space
24. 24. Gravitational Potential Energy <ul><li>For example, one of the masses could be Earth. The other mass could be a rocket. For the diagram above, R 1 could represent the radius of Earth. If the rocket is at rest on Earth, then it does not have any kinetic energy, KE , but only gravitational potential energy, PE g which is equivalent to . </li></ul>Topic 2.1 – Exploration of Space
25. 25. Gravitational Potential Energy <ul><li>The total mechanical energy of the rocket, E T is the sum of the gravitational potential energy and the kinetic energy: E T  = PE g  + KE but at the surface of Earth, the total energy is just the gravitational potential energy: </li></ul><ul><li>E T  = PE g  =  . </li></ul>Topic 2.1 – Exploration of Space
26. 26. Gravitational Potential Energy <ul><li>Now assume that the rocket rises above Earth's surface to a height of R 2 . At this height, it has less gravitational potential energy and some kinetic energy. The total mechanical energy of the rocket remains at the same constant value it had before. </li></ul><ul><li>E T  = KE + PE g  = KE  +  . </li></ul>Topic 2.1 – Exploration of Space
27. 27. Gravitational Potential Energy <ul><li>What is the escape velocity? How is it calculated? </li></ul><ul><li>We can calculate the minimum velocity the rocket must have to escape from Earth's potential well. To do this, the rocket's initial kinetic energy must exceed the depth of the potential well at Earth's surface, thereby making its total energy positive. In the ideal case, this would mean that the rocket must reach an infinite distance where PE g  = 0 before coming to rest. This minimum velocity is called the escape velocity. </li></ul>Topic 2.1 – Exploration of Space
28. 28. Gravitational Potential Energy <ul><li>At the surface of Earth, the total energy is the gravitational potential energy: E T = . </li></ul><ul><li>This energy is changed to kinetic energy: KE r  =   . </li></ul><ul><li>Therefore, </li></ul><ul><li>We take the absolute value of the gravitational potential energy so as to have a positive value for the velocity. For Earth, the escape velocity becomes </li></ul>Topic 2.1 – Exploration of Space
29. 29. Gravitational Potential Energy <ul><li>For Earth, the escape velocity becomes </li></ul><ul><li>Thus a rocket launched from Earth with a velocity greater than this will move away from Earth, losing KE and gaining PE g as it does so. However, since its KE is greater than the depth of its PE g well at any point, its total energy will always remain positive. Theoretically, it will reach an infinite separation distance from Earth with some KE left, and escape. For launch velocity less than the escape velocity, the rocket might come to rest at some finite distance, then fall back to Earth. </li></ul>Topic 2.1 – Exploration of Space
30. 30. Gravitational Potential Energy <ul><li>What is binding energy? How does the binding energy compare in magnitude to the PE g ? </li></ul><ul><li>In order for a rocket to escape from Earth's potential well, its kinetic energy must exceed the gravitational potential energy. If the KE does not exceed the PE g , then the rocket cannot escape from the potential well, and it is said to be “bound” to Earth. The binding energy is the amount of additional kinetic energy it needs to escape. </li></ul>Topic 2.1 – Exploration of Space
31. 31. Gravitational Potential Energy <ul><li>For a rocket at rest on the surface of Earth, the binding energy is identical in magnitude to the gravitational potential energy at the surface of Earth, since at this point, the rocket is not moving. </li></ul><ul><li>E binding = </li></ul>Topic 2.1 – Exploration of Space
32. 32. Gravitational Potential Energy <ul><li>If a rocket is in orbit at any radius R o in the potential well of Earth, then the centripetal force necessary to keep the rocket is the circular orbit is provided by the force of gravitational attraction between the rocket and Earth. If the rocket has a mass m R and an orbital velocity of v R , then </li></ul><ul><li>F c = F g = </li></ul>Topic 2.1 – Exploration of Space
33. 33. Gravitational Potential Energy <ul><li>The total mechanical energy of the orbiting rocket is thus </li></ul><ul><li>This is a very significant result. The total energy of a satellite in a circular orbit at any radius of orbit R o is negative, and is equal to one-half the value of the gravitational potential energy at this radius. The satellite is bound to Earth, and its binding energy is </li></ul>Topic 2.1 – Exploration of Space
34. 34. Newton's Thought Experiment and Satellite Motion . . . Topic 2.2 – Low Earth Orbit . . . leads to Microgravity
35. 35. Micro-Gravity and Apparent Weight Topic 2.2 – Low Earth Orbit
36. 36. Micro-Gravity and Apparent Weight <ul><li>We define the weight of a body as the gravitational force, F g , on the body. But what our bodies feel is really the reaction force of whatever surface we are in contact with (i.e. a chair, the ground, etc.) This upward force that counteracts the force of gravity is the normal force, F N , and it is the apparent weight . </li></ul><ul><li>Micro-gravity can be defined as an environment in which the apparent weight of a system is smaller than its actual weight. Some of the possible environments in which this can occur are an elevator falling freely in a vacuum, a space capsule orbiting the earth, a spacecraft drifting in outer space with its engines off, a roller coaster on a downward path, a parabolic flight on a downward path, and so on. </li></ul>Topic 2.2 – Low Earth Orbit
37. 37. Micro-Gravity and Apparent Weight <ul><li>Imagine standing in an elevator that is at rest. The floor pushes upwards on your feet with the same force that gravity is pulling you down. Your apparent weight is the same as your real weight. </li></ul><ul><li>F N - F g = 0 F N = F g </li></ul>Topic 2.2 – Low Earth Orbit
38. 38. Micro-Gravity and Apparent Weight <ul><li>If the elevator accelerates downwards, the normal force is less and your apparent weight is less. If the elevator accelerates downward at ½ g , then the normal force is reduced to ½ F g and your apparent weight is one-half the force of gravity . </li></ul>Topic 2.2 – Low Earth Orbit
39. 39. Micro-Gravity and Apparent Weight <ul><li>If the elevator is in free fall, then the acceleration is equal to g and the person feels weightless. There is no normal force. </li></ul><ul><li>F N - F g = - ma F N - mg = - mg F N = 0 </li></ul>Topic 2.2 – Low Earth Orbit
40. 40. Micro-Gravity and Apparent Weight Experimentation <ul><li>Your assignment is to research how these 2 concepts allow roller coaster engineers to make the thrill of a roller coaster more exciting. </li></ul>Topic 2.2 – Low Earth Orbit
41. 41. Gravitational Slingshot <ul><li>Interplanetary space probes often make use of then “gravitational slingshot” effect to propel them to high velocities. </li></ul><ul><li>Your assignment is to research this maneuver and explain how a higher velocity is achieved. </li></ul><ul><li>Be prepared to explain how this happens to your classmates. </li></ul>Topic 2.2 – Low Earth Orbit
42. 42. Introduction to Electric Fields <ul><li>Electric fields are created by electric charges, and the fields created by these charges cause other charges to be influenced by them. </li></ul><ul><li>We can define the electric field as the region of space around a charge where a positive test charge experiences a force caused by one or more other charges. </li></ul>Topic 2.3 – Electric & Magnetic Fields
43. 43. Introduction to Electric Fields <ul><li>There are two kinds of charge, positive and negative. Both charges can create an electric field around them . </li></ul><ul><li>Electric field strength, E , can be defined to be the ratio of the electric force, F , to the charge, q , experiencing the force.       </li></ul>Topic 2.3 – Electric & Magnetic Fields
44. 44. Introduction to Electric Fields <ul><li>Electric field lines are lines representing the direction of the electric field. Since electric field is defined to be the electric force per unit charge, the electric field lines are sometimes called lines of force. </li></ul>Topic 2.3 – Electric & Magnetic Fields
45. 45. Electric Field Lines for a Positive Point Charge Topic 2.3 – Electric & Magnetic Fields
46. 46. Electric Field Lines for a Negative Point Charge Topic 2.3 – Electric & Magnetic Fields
47. 47. Electric Field Lines for Two Oppositely Charged Point Charges Topic 2.3 – Electric & Magnetic Fields
48. 48. Electric Field Lines for Two Same Sign Point Charges Topic 2.3 – Electric & Magnetic Fields
49. 49. Electric Field Lines for Two Plates Topic 2.3 – Electric & Magnetic Fields
50. 50. Electric Field Lines for Two Plates & a Positive Charge Topic 2.3 – Electric & Magnetic Fields
51. 51. Electric Field & Electric Force <ul><li>As we have seen, there are two kinds of charge, positive and negative. Now we need to be able to say how much negative or positive charge there is on an object. The internationally accepted SI unit of charge, q , is the coulomb (C) . </li></ul>Topic 2.3 – Electric & Magnetic Fields
52. 52. Electric Field & Electric Force <ul><li>The electric force on the charge q is F e = qE = (+5.00C)(10.0N/C) = +50.0 N </li></ul><ul><li>In general, we can say that the electric field vector and the electric force vector are in the same direction if the charge brought into the field is positive. </li></ul><ul><li>Repulsion </li></ul>Topic 2.3 – Electric & Magnetic Fields
53. 53. Electric Field & Electric Force <ul><li>The electric force on the charge q is F e = qE = (+5.00C)(10.0N/C) = +50.0 N </li></ul><ul><li>In general, we can say that the electric field vector and the electric force vector are in the opposite direction if the charge brought into the field is negative. </li></ul><ul><li>Attraction </li></ul>Topic 2.3 – Electric & Magnetic Fields
54. 54. Electric Field & Electric Force in 1 Dimension <ul><li>If there exists at a place in space, electric fields caused by more than one source, then the fields will add together like vectors since electric field is a vector. </li></ul><ul><li>The total electric field at position P is E T = E 1 + E 2 = 10.0 N/C + (-15.0 N/C) = -5.0 N/C or 5.0 N/C west. If a charge of 2.0 C is placed at position P , then the force on this charge is F = qE T = (2.0 C)(5.0 N/C) = 10. N. The direction of this force is in the same direction as the electric field vector, that is west. </li></ul>Topic 2.3 – Electric & Magnetic Fields
55. 55. Electric Field & Electric Force in 2 Dimension <ul><li>Two electric fields are at right angles relative to each other. The positive charge, q 1 , creates and electric field of 10.0 N/C north while the charge, q 2 , creates and electric field of 15.0 N/C east. </li></ul><ul><li>In adding together the two electric field vectors. We attach them head to tail. </li></ul>Topic 2.3 – Electric & Magnetic Fields
56. 56. Parallel Plates & Millikan Topic 2.3 – Electric & Magnetic Fields
57. 57. Millikan’s Experiment Topic 2.3 – Electric & Magnetic Fields
58. 58. Millikan and the Elementary Charge <ul><li>The currently accepted value for the elementary charge is 1.602 177 33 x 10 -19 C. The value we will use in our calculations is 1.60 x 10 -19 C Thus the total charge, q , on any object is a whole number multiple, N , of this elementary charge, e . q = Ne </li></ul>Topic 2.3 – Electric & Magnetic Fields
59. 59. Gravitational PE vs Electric PE Topic 2.3 – Electric & Magnetic Fields
60. 60. Calculating Electric PE <ul><li>Assume there exists a charge between the plates, (+10.0 C) at a 2.00 cm above the negative plate (h 1 = 0.02 m). </li></ul><ul><li>The positive charge is attracted towards the negative plate and repelled from the positive plate. </li></ul><ul><li>The force the charge experiences is a constant force of F E  = qE towards the plate. Assume that this force is F  = 5.00 N. At the negative plate, the charge does not have any potential energy. </li></ul><ul><li>At a distance of 2.00 cm away from the plate, the potential energy at that location relative to the negative plate is </li></ul><ul><li>PE 1 = Fh 1 = (5.00 N)(0.0200 m) = 0.100 J </li></ul>Topic 2.3 – Electric & Magnetic Fields
61. 61. Calculating Electric PE <ul><li>Now the +10.0 C charge is pulled away from the negative plate towards the positive plate. The force of 5.00 N is used to do this. Suppose that the new distance away from the negative plate is 8.00 cm. The new potential energy of the charge at this location is </li></ul><ul><li>PE 2 = Fh 2 = (5.00 N)(0.0800 m) = 0.400 J </li></ul><ul><li>The charge has a greater potential energy at location B than it did at location A. </li></ul><ul><li>The change in potential energy is </li></ul><ul><li>Δ PE = PE 2 - PE 1 = 0.400 J - 0.100 J = 0.300 J  </li></ul><ul><li>This same amount of energy can be derived from the force-distance graph. The area of the rectangle would be F(Δh) = 5.00 N (0.0800 m - 0.0200 m) = 0.300 J. </li></ul>Topic 2.3 – Electric & Magnetic Fields
62. 62. Work & KE <ul><li>To summarize, the change in electric potential energy of a charge q in moving from A to B is equal to the work required to move q from A to B against the electric field. </li></ul><ul><li>W = ΔPE = PE B – PE A </li></ul><ul><li>If work had to be done to move a charged particle to a higher potential, then when the particle is released and allowed to move freely under the influence of the electric field, the potential energy of the particle will decrease and it will gain in kinetic energy. </li></ul><ul><li>We know that the kinetic energy gained is, KE = ½ mv 2 . If the mass of the charged object is known, then the speed of the object can be found. </li></ul>Topic 2.3 – Electric & Magnetic Fields
63. 63. Electric Potential <ul><li>The electrical potential energy is dependent on the quantity of the charge at a given location. But what if we wanted to measure the amount of energy that is independent of the charge placed at a location? In such a situation, we would have to have a measure of the electric potential energy per unit charge. That quantity is called the electric potential . The symbol “V” is used for electric potential. </li></ul>Topic 2.3 – Electric & Magnetic Fields
64. 64. Electric Potential <ul><li>We can formally define electric potential as follows. </li></ul><ul><li>The electric potential V at a given point is the electrical potential energy, PE , of a test charge q o situated at that point divided by the charge itself. </li></ul><ul><li>The SI unit of electric potential is the joule/coulomb also called the volt (V). </li></ul>Topic 2.3 – Electric & Magnetic Fields
65. 65. Electric Potential <ul><li>The terms electric potential energy , PE , and electric potential , V , have similar names, but they are not the same. Electric potential energy is, as the name implies, a measure of energy, and is therefore measured in joules. In contrast, the electric potential is the quantity of energy per unit charge, and is measured in joules per coulomb, or volts.   </li></ul><ul><li>The term “potential difference” is simply the difference in potential between two points. It also has the units of volts. </li></ul>Topic 2.3 – Electric & Magnetic Fields
66. 66. Calculating the Electric Potential & Potential Difference <ul><li>To calculate the electric potential we use, </li></ul><ul><li>The potential difference between these two points is </li></ul><ul><li>Δ V = V 2 - V 1 </li></ul><ul><li>The change in electric potential energy of a charge q in moving from A to B is equal to the work required to move q from A to B against the electric field. This can now be expressed as follows. </li></ul><ul><li>Δ PE = qV B - qV A = q( V B - V A ) = qΔV </li></ul>Topic 2.3 – Electric & Magnetic Fields
67. 67. The Electron Volt <ul><li>The change in the potential energy of a charge q in moving through electric field can be calculated using ΔPE = qΔV . The traditional unit for energy is the joule (J). However, the joule is not a convenient unit for small charges. Therefore another unit called the “electron volt” is sometimes used.  </li></ul><ul><li>We can define the electron volt as the energy acquired by an electron as a result of moving through a potential difference of 1V. </li></ul><ul><li>Since the magnitude of the charge of an electron is 1.602 x 10 -19 C, and the change in potential energy is qΔV we can say that 1 eV is equal to: </li></ul><ul><li>(1.602 x 10 -19 C)(1V) = 1.602 x 10 -19 J </li></ul>Topic 2.3 – Electric & Magnetic Fields
68. 68. The Relation Between Electric Potential and Electric Field <ul><li>Since the work involved in moving a charge against the electric field </li></ul><ul><li>  </li></ul><ul><li>between two plates is W = qΔV and , another way of determining the work is </li></ul><ul><li>W = qEd . </li></ul>Topic 2.3 – Electric & Magnetic Fields
69. 69. Equipotential Lines <ul><li>Electric potential can be represented in a diagram by drawing equipotential lines. An equipotential line is one where all points on that line are at the same potential. That is, the potential difference between any two points on the line is zero. Because of this, no work is required to move a charge from one point to another. </li></ul>Topic 2.3 – Electric & Magnetic Fields
70. 70. Electrical Potential Video Topic 2.3 – Electric & Magnetic Fields
71. 71. Electric Potential & Potential Energy for a Point Charge <ul><li>Gravitational Potential Energy for Two Masses </li></ul><ul><li>Electric Potential Energy for Point Charges </li></ul>Topic 2.3 – Electric & Magnetic Fields
72. 72. Electric Potential Energy for Point Charges <ul><li>It is important to realize that the “zero” of potential energy occurs when the point charges are very far apart, in fact when they are at an infinite separation distance. </li></ul>Topic 2.3 – Electric & Magnetic Fields
73. 73. Electric Potential for Point Charges Topic 2.3 – Electric & Magnetic Fields
74. 74. Electric Potential for a Positive Point Charge Topic 2.3 – Electric & Magnetic Fields
75. 75. Electric Potential for a Negative Point Charge Topic 2.3 – Electric & Magnetic Fields
76. 76. Total Electric Potential <ul><li>We have seen that a single point charge can raise or lower the electric potential at a given location depending on whether the charge is positive or negative. If there are two or more charges, then we should follow the following rule to determine the total potential. </li></ul><ul><li>When two or more charges are present, the potential due to all the charges is obtained by adding together the individual potentials. </li></ul>Topic 2.3 – Electric & Magnetic Fields
77. 77. Total Electric Potential Topic 2.3 – Electric & Magnetic Fields
78. 78. Lines of Equipotential <ul><li>Equipotential lines are perpendicular to electric field lines. We can also apply these ideas to point charges. </li></ul>Topic 2.3 – Electric & Magnetic Fields
79. 79. Potential Energy, Kinetic Energy, and Electric Field: Example <ul><li>The diagram shows a negatively charged drop moving between two deflecting plates between which a uniform, downward-pointing electric field, E , has been set up. The drop is deflected upward and then strikes the paper at a position that is determined by the strength of the electric field and the charge on the drop. </li></ul>Topic 2.3 – Electric & Magnetic Fields
80. 80. A Charged Particle Moving at Constant Acceleration: Example Topic 2.3 – Electric & Magnetic Fields
81. 81. Magnetic Fields Topic 2.3 – Electric & Magnetic Fields
82. 82. Magnetic Fields Topic 2.3 – Electric & Magnetic Fields
83. 83. Ferromagnetism <ul><li>Some materials, such as iron, nickel, cobalt, and gadolinium, are not normally magnetized, but under certain circumstances, they can become magnetized. Such materials are called ferromagnetic . </li></ul><ul><li>Ferromagnetic materials are strongly attracted by magnets. Ferromagnetic substances are commonly referred to as “magnetic substances.” </li></ul>Topic 2.3 – Electric & Magnetic Fields
84. 84. Domain Theory of Magnetism <ul><li>How ferromgnetic substances are able to acquire magnetic properties may be explained using the Domain Theory of Magnetism . </li></ul><ul><li>Ferromagnetic substances are composed of a large number of tiny regions (less than 1 micrometer long or wide) called “magnetic domains.” </li></ul><ul><li>Each domain behaves like a tiny bar magnet, with its own north and south poles. When the material is in an unmagnetized state, these millions of domains are oriented at random, so that their magnetic effects cancel out. </li></ul>Topic 2.3 – Electric & Magnetic Fields
85. 85. Domain Theory of Magnetism <ul><li>In the diagram below, the arrows represent the domains in a small piece of unmagnetized iron. </li></ul>Topic 2.3 – Electric & Magnetic Fields
86. 86. Domain Theory of Magnetism <ul><li>However, if a piece of ferromagnetic material such as iron is placed in a strong enough magnetic field, a strange phenomenon occurs. Some domains actually rotate slightly to align with the external field while others that are already aligned tend to grow at the expense of other non-aligned domains. The net result is that there is a preferred orientation of the domains in the same direction as the external field, causing the material to behave like a magnet . </li></ul>Topic 2.3 – Electric & Magnetic Fields
87. 87. The Magnetic Field of the Earth Topic 2.3 – Electric & Magnetic Fields
88. 88. The Magnetic Field of the Earth <ul><li>We will define the north magnetic pole as the pole that is found in the northern hemisphere. This pole acts as though it is a south pole on a bar magnet. The north magnetic pole is so named because it is the location toward which the north end of a compass needle points. </li></ul><ul><li>The south magnetic pole is the pole that is in the southern hemisphere. This pole acts like the north pole of a bar magnet. The north end of a compass points away from this pole. At the poles, a magnetic compass would just rotate freely. </li></ul>Topic 2.3 – Electric & Magnetic Fields
89. 89. The Magnetic Field of the Earth <ul><li>The north geographic pole is that point where the earth’s axis of rotation crosses the surface in the northern hemisphere. The north magnetic pole does not coincide with the north geographic pole, but instead lies in Hudson Bay some 1300 km to the south. The south magnetic pole is located in Antarctica near the Ross Sea. The axis of the fictitious bar magnet and the earth’s rotational axis is about 11.5 o . </li></ul>Topic 2.3 – Electric & Magnetic Fields
90. 90. Magnetic Declination and Magnetic Inclination <ul><li>The north magnetic pole does not coincide with the north geographic pole, but instead lies in Hudson Bay some 1300 km to the south. The south magnetic pole is located in Antarctica near the Ross Sea. Magnetic declination is the angle between magnetic north and geographic north and varies from position to position on the earth’s surface. Magnetic inclination or angle of dip is the angle between the earth’s magnetic field at any point and the horizontal, is called the magnetic inclination and it is measured with a magnetic dipping needle. </li></ul>Topic 2.3 – Electric & Magnetic Fields
91. 91. The Magnetosphere and the Auroras <ul><li>The magnetosphere is a region of the upper atmosphere beyond approximately 200 km in which the motion of charged particles from space is governed by the magnetic field of the earth. The magnetosphere on the side facing the sun extends beyond the earth’s surface approximately 57 000 km or about 10 earth radii. On the side away from the sun, the magnetosphere probably extends outward for hundreds of earth radii. The elongated shape results from the influence of the onrushing solar wind . The solar wind consists mainly of protons and electrons emitted by the sun, and this compresses the magnetosphere on the side nearest the sun. </li></ul>Topic 2.3 – Electric & Magnetic Fields
92. 92. The Magnetosphere and the Auroras Topic 2.3 – Electric & Magnetic Fields
93. 93. The Magnetosphere and the Auroras Topic 2.3 – Electric & Magnetic Fields
94. 94. The Magnetosphere and the Auroras <ul><li>Auroras , commonly called the northern or southern lights, are caused by high energy particles from the solar wind that are trapped in the Van Allen belts of the earth’s magnetic field. As these particles oscillate along the magnetic field lines, they enter the atmosphere near the north and south magnetic poles. Energetic electrons collide with the oxygen and nitrogen molecules in the atmosphere. These collisions excite the molecules. When they escape from their excited states, they emit the light we see in the auroras. This forms a curtain of light that may hang down to an altitude of 100 km. Green light is emitted by oxygen, and pink light by nitrogen, but often the light is so dim that only white light can be seen. </li></ul>Topic 2.3 – Electric & Magnetic Fields
95. 95. The Magnetosphere and the Auroras Topic 2.3 – Electric & Magnetic Fields