1 00:00:04,890 --> 00:00:09,920 Air is normally an insulator, but under certain conditions, it can suddenly and temporarily 2 00:00:09,920 --> 00:00:15,039 change into a conductor, and we end up with a spark. In this video, we'll use the related 3 00:00:15,039 --> 00:00:21,380 concepts of electric fields and electric potential to explain how insulators can suddenly, dramatically 4 00:00:21,380 --> 00:00:24,570 and temporarily become conductors. 5 00:00:24,570 --> 00:00:31,570 This video is part of the Derivatives and Integrals video series. 6 00:00:33,150 --> 00:00:40,150 Hello. My name is John McGreevy. I am a professor in the physics department at MIT, and today 7 00:00:43,829 --> 00:00:48,239 I'll be talking with you about the electric field and electrical potential. 8 00:00:48,239 --> 00:00:52,620 To get the most out of this video you should already have some exposure to the electric 9 00:00:52,620 --> 00:00:56,429 field and electric potential. You should be able to take a mathematical expression for 10 00:00:56,429 --> 00:01:02,960 the field and obtain the potential, and vice versa. You should also know how to draw equipotential 11 00:01:02,960 --> 00:01:06,280 surfaces and electric field vectors. 12 00:01:06,280 --> 00:01:10,200 Throughout this video our goal is to help you gain a clearer picture of the electric 13 00:01:10,200 --> 00:01:14,490 field and the electric potential. By the end of the video you should also be able to describe 14 00:01:14,490 --> 00:01:19,229 the process of electrical breakdown by using either the field or the potential. 15 00:01:19,229 --> 00:01:23,280 Let's start with a review of electric field and electric potential. First we'll describe 16 00:01:23,280 --> 00:01:27,649 them conceptually. Then we'll show the mathematical relationship between them, and show some of 17 00:01:27,649 --> 00:01:30,320 their typical visual representations. 18 00:01:30,320 --> 00:01:36,090 First, let's see what you remember. Take out a piece of paper and write down everything 19 00:01:36,090 --> 00:01:40,189 you remember about the electric field and the electric potential. Try to concentrate 20 00:01:40,189 --> 00:01:47,189 on their similarities and differences. Pause the video to do this. 21 00:01:49,490 --> 00:01:52,869 Now you can compare the list you made to our list. 22 00:01:52,869 --> 00:01:56,759 The electric field is generated by electric charges, and extends an infinite distance 23 00:01:56,759 --> 00:01:57,750 from them. 24 00:01:57,750 --> 00:02:01,289 If you bring a second electric charge into a region of electric field, there will be 25 00:02:01,289 --> 00:02:07,920 a force exerted on it. Like all forces, that force has magnitude and direction. The stronger 26 00:02:07,920 --> 00:02:10,728 the charge is, the more force will be applied to it. 27 00:02:10,728 --> 00:02:16,390 The electric field is a vector quantity. It has a vector value at every point in space, 28 00:02:16,390 --> 00:02:19,819 measured in Newtons per Coulomb or Volts per Meter. 29 00:02:19,819 --> 00:02:24,640 Much like the electric field, electric potentials are created by charges and extend an infinite 30 00:02:24,640 --> 00:02:26,290 distance from them. 31 00:02:26,290 --> 00:02:30,200 If you bring a second charge into a region of electrical potential, that second charge 32 00:02:30,200 --> 00:02:35,720 will gain or lose potential energy. The stronger that charge, the more its potential energy 33 00:02:35,720 --> 00:02:36,989 will change. 34 00:02:36,989 --> 00:02:41,680 Unlike the electric field, the electric potential is a scalar quantity, which means that everywhere 35 00:02:41,680 --> 00:02:48,680 you look you can find a number that represents the potential, measured in Joules per Coulomb. 36 00:02:48,840 --> 00:02:52,540 Let's look at two ways to envision an electric potential for a positively charged line near 37 00:02:52,540 --> 00:02:57,599 the origin. We're going to look at this in two dimensions to make things easier to see. 38 00:02:57,599 --> 00:03:01,750 We can also draw the level curves for the electric potential function. These are called 39 00:03:01,750 --> 00:03:06,060 "equipotential lines," because the value of the potential is equal at every point on a 40 00:03:06,060 --> 00:03:11,769 given line. For instance, we might draw lines every ten volts. 41 00:03:11,769 --> 00:03:16,450 If we plot the potential on the vertical axis, we end up with this mountain-like shape. We 42 00:03:16,450 --> 00:03:20,349 can imagine positive charges rolling down the mountain as they are pushed away from 43 00:03:20,349 --> 00:03:22,299 our line charge. 44 00:03:22,299 --> 00:03:27,420 We can also sketch the electric field around a line charge. If we pick regularly spaced 45 00:03:27,420 --> 00:03:31,790 points at which to draw our electric field vectors, we end up with a picture like this 46 00:03:31,790 --> 00:03:38,250 one. Each vector shows the direction and strength of the electric field at that point. The longer 47 00:03:38,250 --> 00:03:43,610 the arrow, the stronger the field is. Here you might imagine the arrows pushing a positive 48 00:03:43,610 --> 00:03:46,840 charge away from our line 49 00:03:46,840 --> 00:03:52,909 Displaying both the equipotential lines and the field vectors at once, we get this picture. 50 00:03:52,909 --> 00:03:59,099 You can see that the equipotential lines are always perpendicular to the field. 51 00:03:59,099 --> 00:04:03,879 Since charges create both fields and potentials, both will be present all the time, though 52 00:04:03,879 --> 00:04:06,700 we might only draw one or the other. 53 00:04:06,700 --> 00:04:12,110 The field and the potential are related mathematically through the gradient operator. As a vector 54 00:04:12,110 --> 00:04:19,079 operator, the gradient turns the scalar potential into a vector field. To go in the other direction, 55 00:04:19,079 --> 00:04:24,170 a line integral of the electric field turns that vector field into the scalar electric 56 00:04:24,170 --> 00:04:26,160 potential. 57 00:04:26,160 --> 00:04:31,110 The negative sign that appears in both equations is important—the electric field points in 58 00:04:31,110 --> 00:04:36,720 the opposite direction from any changes in the potential. If the electric potential increases 59 00:04:36,720 --> 00:04:41,940 in a particular direction, the electric field points in the opposite direction. 60 00:04:41,940 --> 00:04:47,080 We're going to use something called "electrical breakdown" to illustrate our concepts today. 61 00:04:47,080 --> 00:04:53,500 We'll start with an example, give a definition, then go into an explanation of the phenomenon. 62 00:04:53,500 --> 00:05:00,500 Here is a clip from the Boston Museum of Science to demonstrate 63 00:05:08,610 --> 00:05:15,610 the phenomenon. 64 00:06:32,990 --> 00:06:37,050 Quite a dramatic demonstration! Let's look at this in a little more depth. 65 00:06:37,050 --> 00:06:42,630 Electrical breakdown is defined as the process by which an insulating material in a strong 66 00:06:42,630 --> 00:06:48,530 electric field becomes electrically conductive. The material actually changes from being an 67 00:06:48,530 --> 00:06:53,780 insulator to being a conductor. In the clip you saw, this happened in the air near the 68 00:06:53,780 --> 00:06:58,600 Van de Graaff generator, and a large electric spark resulted. 69 00:06:58,600 --> 00:07:02,520 You may sometimes hear this referred to as breakdown potential, or breakdown voltage, 70 00:07:02,520 --> 00:07:05,290 which is the same thing. 71 00:07:05,290 --> 00:07:10,790 The exact value of the electric field needed depends on many factors, including distance, 72 00:07:10,790 --> 00:07:14,030 humidity, temperature, and the material itself. 73 00:07:14,030 --> 00:07:20,250 Here is a simplified explanation of how electrical breakdown works in air. Consider this house 74 00:07:20,250 --> 00:07:22,860 in a thunderstorm. 75 00:07:22,860 --> 00:07:29,060 If we zoom in on the air above the house, we can see the molecules of gas in the air. 76 00:07:29,060 --> 00:07:34,810 Thunderstorms involve strong electric fields and high electric potential differences. We 77 00:07:34,810 --> 00:07:38,560 can represent those on our diagram. 78 00:07:38,560 --> 00:07:43,500 Imagine that one electron is pulled from its atom by the strong electric field. Because 79 00:07:43,500 --> 00:07:48,190 the electron is negatively charged, it will accelerate against the electric field, and 80 00:07:48,190 --> 00:07:52,800 will eventually collide with another atom. That collision might knock another electron 81 00:07:52,800 --> 00:07:57,180 loose. Now there will be two electrons accelerating. 82 00:07:57,180 --> 00:08:03,310 A single electron can thus create a chain reaction, where many atoms lose their electrons. 83 00:08:03,310 --> 00:08:08,460 This creates a region of ionized air. Air is normally a good insulator, but the presence 84 00:08:08,460 --> 00:08:11,120 of ions allows it to conduct electricity. 85 00:08:11,120 --> 00:08:14,070 ...resulting in a lightning bolt! 86 00:08:14,070 --> 00:08:19,120 Let's use the electric field and electric potential to investigate this situation further. 87 00:08:19,120 --> 00:08:22,980 Here are the Van de Graaff generators from the video, charged up, with a metal ball as 88 00:08:22,980 --> 00:08:25,220 a target. 89 00:08:25,220 --> 00:08:29,690 Let's take a simplified version of the situation shown. Draw the equipotential surfaces around 90 00:08:29,690 --> 00:08:35,510 these two objects, and then draw in the electric field arrows as well. You can ignore the presence 91 00:08:35,510 --> 00:08:37,610 of the support pillars. 92 00:08:37,610 --> 00:08:42,530 Here are two hints. First, the small metal ball is grounded, or "earthed," with an electrical 93 00:08:42,530 --> 00:08:47,690 potential of zero. Second, the electrical charge on the generator will spread itself 94 00:08:47,690 --> 00:08:51,740 equally over the surface of the conducting spheres. 95 00:08:51,740 --> 00:08:58,740 Pause the video here to draw the equipotential lines and the field vectors. 96 00:08:59,560 --> 00:09:03,620 Here's another picture of the generator with the target ball nearby. 97 00:09:03,620 --> 00:09:09,120 This picture is too complex. Let's create a simpler version of the picture. That's 98 00:09:09,120 --> 00:09:14,380 Now we can draw in the lines. Our equipotential lines will "hug" the surface of the conductors 99 00:09:14,380 --> 00:09:19,930 when they are nearby. Because the charge is spread evenly across the surface of the conductor, 100 00:09:19,930 --> 00:09:23,990 the whole surface will be at the same electric potential. The equipotential lines will tend 101 00:09:23,990 --> 00:09:27,530 to be smoother when farther away from the conductors. 102 00:09:27,530 --> 00:09:31,620 Because the electric potential of the Van de Graaff generator gets up to about one million 103 00:09:31,620 --> 00:09:37,110 volts (or 1000 kilovolts), and we have drawn eight lines in the picture, each line must 104 00:09:37,110 --> 00:09:41,110 represent a difference of about 125 kilovolts. 105 00:09:41,110 --> 00:09:45,670 In this view we have colored in the regions where the equipotential lines are more closely 106 00:09:45,670 --> 00:09:48,640 packed, or less closely packed. 107 00:09:48,640 --> 00:09:55,090 In the blue area, with the close-packed lines, the gradient of the potential is larger. Because 108 00:09:55,090 --> 00:09:58,840 the electric field is proportional to the gradient of the potential, the places where 109 00:09:58,840 --> 00:10:03,390 our lines are more closely packed will have a stronger electric field. 110 00:10:03,390 --> 00:10:08,260 In the red areas, where equipotential lines are far apart, the gradient of the potential 111 00:10:08,260 --> 00:10:12,630 is smaller. Therefore, the electric field will be weaker. 112 00:10:12,630 --> 00:10:15,870 We can use this as a guide when drawing our field vectors. 113 00:10:15,870 --> 00:10:19,740 Let's draw in those electric field vectors now. We have assumed here that the generator 114 00:10:19,740 --> 00:10:23,900 becomes positively charged, but if it were negatively charged, we could simply reverse 115 00:10:23,900 --> 00:10:26,320 the direction of our arrows. 116 00:10:26,320 --> 00:10:32,050 Look carefully: our field arrows are perpendicular to the equipotential surfaces at all points. 117 00:10:32,050 --> 00:10:35,970 Check your own diagram - is this true on yours as well? 118 00:10:35,970 --> 00:10:40,770 Our field arrows are longer where the equipotential lines are more closely packed—is this true 119 00:10:40,770 --> 00:10:42,710 on your diagram? 120 00:10:42,710 --> 00:10:48,140 If you need to revise your diagram or draw a new one, do so now. If you have questions 121 00:10:48,140 --> 00:10:50,680 for your teacher, here is a chance to ask them. 122 00:10:50,680 --> 00:10:57,110 Pause the video here. 123 00:10:57,110 --> 00:11:01,390 Some of you may be confused by the terminology that is used for this phenomenon. Many people 124 00:11:01,390 --> 00:11:06,940 refer to the "breakdown potential" required to create a spark. However, but you may have 125 00:11:06,940 --> 00:11:11,220 noticed that the sparks in the video were produced where the electric field was the 126 00:11:11,220 --> 00:11:16,060 strongest, not where the electric potential was the highest. Turn to a friend and discuss 127 00:11:16,060 --> 00:11:23,060 why this is the case. Pause the video here to discuss. 128 00:11:23,320 --> 00:11:26,750 If we return to the equations that relate the field and the potential, we can improve 129 00:11:26,750 --> 00:11:32,610 our understanding. You can see that we have a gradient term—a derivative with respect 130 00:11:32,610 --> 00:11:33,330 to distance. 131 00:11:33,330 --> 00:11:39,120 If our potential changes slowly over distance, the field is weak, and no spark is generated. 132 00:11:39,120 --> 00:11:44,880 On the other hand, if the potential changes quickly over distance, the field is strong. 133 00:11:44,880 --> 00:11:48,370 A stronger field is more likely to remove an electron from an atom. 134 00:11:48,370 --> 00:11:52,790 In fact, when numerical values are given for the breakdown potential, they are most often 135 00:11:52,790 --> 00:11:58,420 given in "volts per meter," which is a measurement of the electric field. The term "breakdown 136 00:11:58,420 --> 00:12:02,130 potential" is a little misleading, but it is still the standard terminology. 137 00:12:02,130 --> 00:12:08,540 To review, the gradient connects the electric field to the electric potential. A steeper 138 00:12:08,540 --> 00:12:13,940 change in the potential results in a stronger electric field. We also saw that electrical 139 00:12:13,940 --> 00:12:20,940 breakdowns happen in areas of strong electric field, or of steep change in electrical potential. 140 00:12:21,310 --> 00:12:26,250 We hope you enjoyed this clip from the Theatre of Electricity at the Boston Museum of Science. 141 00:12:26,250 --> 00:12:32,190 Good luck in your future studies of electricity.