air is normally an insulator but under certain conditions it can suddenly and temporarily change into a conductor and we end up with a spark in this video we'll use the related concepts of electric fields and electric potential to explain how insulators can suddenly dramatically and temporarily become conductors this video is part of the derivatives and integrals video series derivatives and integrals are used to analyze the properties of a system derivatives describe local properties of systems and integrals quantify their cumulative properties hello my name is John McGreevy I'm a professor in the physics department at MIT and today I'll be talking with you about the electric field and electric potential to get the most out of this video you should already have some exposure to the electric field an electric potential you should be able to take a mathematical expression for the field and obtain the potential and vice-versa you should also know how to draw equipotential surfaces and electric field vectors throughout this video our goal is to help you gain a clearer picture of the electric field and the electric potential by the end of the video you should be able to describe the process of electrical breakdown by using either the field or the potential let's start with a review of electric field and electric potential first we'll describe them conceptually then we'll show the mathematical relationship between them and show some of their typical visual representations first let's see what you remember take out a piece of paper and write down everything you remember about the electric field and the electric potential try to concentrate on their similarities and differences pause the video to do this now you can compare the list you made to our list the electric fields generated by electric charges and extends an infinite distance from them if you bring a second electric charge into a region of electric field there will be a force exerted on it like all forces that force has a magnitude and a direction the stronger the charges the more force will be applied to it the electric field is a vector quantity it has a vector value at every point in space measured in Newton's per Coulomb or volts per meter much like the electric field electric potentials are created by charges and extend an infinite distance from them if you bring a second charge into a region of electrical potential that second charge will gain or lose potential energy the stronger that charge the more its potential energy will change unlike the electric field the electric potential is a scalar quantity which means that everywhere you look you can find one number that represents the potential measured in joules per Coulomb let's look at two ways to envision an electric potential for a positively charged line near the origin we're going to look at this in two dimensions to make things easier to see we can draw the level curves for the electric potential function these are called equipotential lines because the value of the potential is equal at every point on a given line for instance we might draw lines every 10 volts if we plot the potential on the vertical axis we end up with this mountain like shape we can imagine positive charges rolling down the mountain as they're pushed away from our line charge we can also sketch the electric field around a line charge if we pick regularly spaced points at which to draw our electric field vectors you end up with the picture like this one each vector shows the direction and strength of the electric field at that point the longer the arrow stronger the field is here you might imagine the arrow is pushing a positive charge away from our line charge displaying both the equipotential lines and the field vectors at once we get this picture you can see that the equipotential lines are always perpendicular to the field since charges create both fields and potentials both will be present all the time though we might only draw one or the other the field and potential are related mathematically through the gradient operator as a vector operator the gradient turns the scalar potential into a vector field to go in the other direction a line integral of the electric field turns that vector field into a scalar electric potential the negative sign that appears in both equations is important the electric field points in the opposite direction from any changes in the potential if the electric potential increases in a particular direction the electric field points in the opposite direction we're going to use something called electrical breakdown to illustrate our concepts today we'll start with an example give a definition then go into an explanation of the phenomenon here's a clip from the Boston Museum of Science to demonstrate the phenomenon a Van de Graaff generator it is actually the world's largest air insulated Van de Graaff generator it was built by dr. Robert Van de Graaff himself you that's quite a dramatic demonstration let's look at this in a little more depth electrical breakdown is defined as the process by which an insulating material in a strong electric field becomes electrically conductive the material actually changes from being an insulator to being a conductor in the clip you saw this happened in the air near the Van de Graaff generator and a large electric spark resulted you may sometimes hear this referred to as breakdown potential or breakdown voltage which is the same thing the exact value of the electric field needed depends on many factors including distance humidity temperature and the material itself here is a simplified explanation of how electrical breakdown works in air consider this house in a thunderstorm if we zoom in on the air above the house we can see the molecules of gas in the air thunderstorms involve strong electric fields and high electric potential differences we can represent those on our diagram imagine that one electron is pulled from its atom by the strong electric field because the electron is negatively charged it will accelerate against the electric field and will eventually collide with another atom that collision might knock another electron loose now there will be two electrons accelerating so a single electron can create a chain reaction where many atoms lose their electrons this creates a region of ionized air air is normally a good insulator but the presence of those ions allows it to conduct electricity resulting in a lightning bulb let's use the electric field an electric potential to investigate the situation further here are the Van de Graaff generators from the video charged up with a metal ball as a target let's take a simplified version of the situation shown draw the equipotential surfaces around these two objects and then draw in the electric field arrows as well you can ignore the presence of the support pillars here are two hints first the small metal ball is grounded or earth with an electrical potential zero second the electrical charge on the generator will spread itself equally over the surface of the conducting spheres pause the video here to draw the equipotential lines and the field vectors here's another picture of the generator with the target ball nearby this picture is too complex let's create a simpler version of the picture that's better now we can draw in the lines our equipotential lines will hug the surface of the conductor's when they're nearby because the charge is spread evenly across the surface of the conductor the whole surface will be at the same electric potential the equipotential lines will tend to be smoother when farther away from their conductors because the electric potential of the vandegraaff generator gets up to about 1 million volts or a thousand kilovolts and we have drawn eight lines in the picture each line must represent a difference of about 125 kilovolts in this view we have colored in the regions where the equipotential lines are either more closely packed or less closely packed in the blue area with the close packed lines gradient of the potential is larger because the electric field is proportional to the gradient of the potential the places where our lines are more closely packed will have a stronger electric field in the red areas or equipotential lines are far apart the gradient of the potential is smaller therefore the electric field will be weaker we can use this as a guide when drawing our field vectors let's draw in those electric field vectors now we have assumed here that the generator becomes positively charged but if it were negatively charged we could simply reverse the direction of our arrows look carefully our field arrows are perpendicular to the equipotential surfaces at all points check your own diagram is this true in yours as well our field arrows are longer where the equipotential lines are more closely packed is this true on your diagram if you need to revise your diagram or draw a new one do so now if you have questions for your teacher here's a chance to ask them pause the video here some of you may be confused by the terminology that's used for this phenomenon many people are refer to the breakdown potential required to create a spark however you may have noticed that the sparks in the video were produced where the electric field was the strongest not where the electric potential was the highest turn to a friend and discuss why this is the case pause the video here to discuss if we return to the equations that relate the field and the potential we can improve our understanding you can see that we have a gradient term a derivative with respect to distance if our potential changes slowly over distance the field is weak and no spark is generated on the other hand if the potential changes quickly over distance the field is strong a stronger field is more likely to remove an electron from an atom in fact when numerical values are given for the breakdown potential they're often given in volt per meter which is actually a measurement of the electric field the term breakdown potential is a little misleading but it's still the standard terminology to review the gradient connects the electric field to the electric potential a steeper change in the potential results in a stronger electric field we also saw that electrical breakdowns happened in areas of strong electric field or a steep change in the electrical potential we hope you enjoyed this clip from the Theater of electricity at the Boston Museum of Science good luck in your future studies of electricity
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