Electric Fields - A Level Physics

hello today we're continuing our a level physics revision series looking at fields and in particular we are looking at electric fields you need to see the previous video for information on what fields are and what gravitational fields do there is an electric field in the presence of a charged object so if you have an object that let's say it's positively charged then there will be a field which will act radially now the direction of the field depends on what the charges for gravitational field remember the field always acted in words but for an electric charge it depends if it's a positive charge then the field will act outwards but if it's a negative charge then the field will act in words but it'll be one or the other not both as I appear to show here on the other hand if you have two plates where one plate is positively charged and the other plate is negatively charged then the field always goes from positive to negative and that will be the electric field and that field as we said in the previous video is the capability to do something and in this case it's the capability to act with a force on a charge so if you were to put let's say a positive charge in that field then that charge would accelerate towards the negative plate if you were to put a negative charge particle in the field then of course it would accelerate towards the positive plate if you take two charges let's call them Q 1 and Q 2 and they are a distance R apart then there will be a force acting between those two charges and that force equals Q 1 times Q 2 in other words the value of the two charges multiplied together divided by 4 PI epsilon naught R squared where R is the distance the charges epsilon-naught is what is called the permittivity of free space or if you've got an actual material between the charges it will be the permittivity of that material but most of the time we've got either air or vacuum and for all practical purposes they are the same epsilon naught has a value it's the permittivity of free space and that is eight point eight five times ten to the minus twelve and then the unit's can vary sometimes it's coulombs squared per Newton per meter squared which of course is what you need to be dimensionally consistent because the force will be in Newtons the charge will be in coulombs and since there's two of them it'll be coulombs squared and R squared will be in meters squared so in order for this to be dimensionally consistent epsilon naught has to be in terms of coulombs squared per meter or per Newton per meter squared but you will also find that described as eight point eight five times ten to the minus twelve the value is the same but the units are farads per meter and you'll find that when we deal with capacitance if you look at the videos on capacitance essentially that unit is the same as that unit now what is actually happening here well each of these charges has an electric field associated with it and those electric fields will have an impact on any charged particle that may come into contact with the field so here we have a charged particle with a field and here's another charged particle in the presence of this one's field and so it will have an attraction or a repulsion depending on whether it's positive or negative on the basis of the field generated by that charged particle equally this charged particle is generating a field and this charged particle is in that one's field so that also experiences force and consequently the to experience a force as a consequence of the field of the other and that force is given by that equation now the electric field strength is given by the force per unit charge and so e equals F over Q and if we say that for example Q 2 is our unit charge Q that means that E is equal to Q 1 divided by 4 PI epsilon naught R squared because Q 2 is Q and F divided by Q will give you Q 1 over 4 PI epsilon naught R squared that's the value of the electric field strength now we come to the concept of electric potential energy and the electric potential energy is the work done to bring a test charge little Q from infinity to a point R away from a main charge so here's a main charge which we're going to call Q 1 and we have got an electron right the way out here we're all here let's call that infinity and we're going to bring that charge to here now if it's the same charge if it's positively charged remember that like poles repel unlike poles attract like charges repel unlike charges attract so if this is positive and the charge out here which is little Q is also positive then there will be a repulsive force and that will push that little Q away so if we want to bring Q 2 here then we're going to have to do work to overcome the repulsive force so we're bringing little Q all the way along to this point here and when it's here it will be R away from Q 1 and the energy the electric potential energy to bring that force sorry to bring that charge to that point overcoming the repulsive is equal to Q Q which is this charge that's q1 times the test charge little Q divided by four PI epsilon naught R naught R squared is up here but now just single R and that means that when R is infinity that is when the test charge was infinitely far away then the potential energy EP is equal to zero this is the potential energy and that's the energy required to bring a test charge from infinity to a point R away from the main charge Q 1 now the electric potential is the potential energy per unit charge and that's given the term V and we express that in volts and that's ep the potential energy divided by Q and if you take EP divided by Q then that's simply Q 1 divided by 4 PI epsilon naught R and that as I've said is expressed in volts now let's give an example of how that applies let's think of two plates rather like a capacitor if you like and we have 400 volts on that plate and North volts on that plate we could achieve that by connecting it to a battery would have to be a pretty big battery for 400 volts but they are sort of those around the wrong way so the positive side is here the negative side is here this is 400 volts because the battery is 400 volts and there's 400 volts on that plate naught on that plate and they will therefore be an electric field because this plate is positively charged this plate is negatively charged there is an electric field and the voltage between the two plates V is 400 volts the field strength of course is the same everywhere between the plates II does not change but the voltage is going to change because on the plate here it's 400 volts on the plate here at zero and so between the plates the voltage drops here it's 300 volts here it's 200 volts here if I drew another line it would be 100 volts and then zero so the voltage is falling as you go further between this plate and this plate but the electric field remains the same the electric field is V divided by D that's constant the V is changing but so is d changing in other words the distance between the four hundred and there is that full amount there the distance between three hundred and zero is three-quarters of D and so the e field stays the same it's the voltage that changes so now let's just compare and contrast gravitational and electric fields to see where they're the same and where they are different let's take the earth and let's take a positive charge cube what do we know well firstly we know that as far as the gravitational field is concerned it always points inwards whereas the field for charge depends on whether the charge is positive or negative for a positive charge as we have here it points outwards but if it were a negative charge then it would point inwards you cannot shield yourself from a gravitational field gravitational fields apply through everything whereas you can shield yourself from an electric charge by using some kind of insulator or maybe an electric screen that will divert the effect of the field a gravitational field is not affected by anything you put between the object in the field and the mass that's attracting it whereas the field operating for an electric charge is certainly affected by something you put between it for example that's why a dielectric which is piece of insulating material has a significant impact in a capacitor look at my video on capacitors and dielectrics to see the consequence of that what is the impact on energy well in a gravitational field let's take two positions this is the ground and we're going to take a position that's a distance H above the ground here is an object being held above the ground a distance H it will have potential energy equaling m the mass of the object times G the gravitational attraction times H this is true for near Earth it wouldn't be true if you were well away from the earth because little G would then have change but near the earth within the first hundred meters or so this is not a bad approximation the potential energy is mg H if you then drop that body it will accelerate towards the earth and just before it hits on the earth it will be traveling at speed V and it will have a kinetic energy of 1/2 MV squared and what you can say is that 1/2 MV squared equals MGH because the potential energy will simply have been converted into kinetic energy the M's cancel and so half V squared equals G H that enables you to calculate the velocity that that object will hit the earth by contrast if you have two parallel plates and they are a distance D apart and you have a positively charged charged little Q that will accelerate towards the negative plate and what we've shown is that the electric field is equal to V divided by D that's what we showed up here but we also know that that equals force divided by charge because that's how we define let's see if we can find that here is the electric field is the force divided by charge and here the electric field is the volts divided by distance or the potential divided by distance so we've got now two formally for the electric field V divided by DVS volts D is the distance between the plates and F divided by Q the force between the charged particles and the unit charge value and if you multiply those out then you can say that V Q equals F D but what is Force Times distance Force Times distance is a measure of the work done or the energy and so now we see why VQ is a measure of energy and to take that a little bit further if we say that energy I'm going to call that en to distinguish it from the field the energy is equal to V Q then power equals energy divided by time and that means V Q divided by T but what is Q over T the amount of charge moved in a particular time is current and that equals VI and that's why the power in an electric circuit is equal to the voltage times the current for both gravitational fields and electric fields the potential energy is zero when the distance from the object or charge is infinity and if you have let's say a mass of the earth here and on this side we're going to have a charge Q and you have a test mass M which you move from here to here so that's position one that's a later position position two and here you have a test charge and you move it to here so the charge moves from here to here this is distance R 2 this is distance R 1 and similarly here this is distance R 1 this is distance R 2 and what you can say is that the difference in potential energy between the mass at this point and the mass at that point is equal to G M M into 1 minus sorry 1 over R 1 squared minus 1 over R 2 squared and here the difference in potential energy is equal to Q 1 Q 2 divided by 4 PI epsilon naught where epsilon naught is the permittivity of free space into I hope I can squeeze this on so you can see it 1 over R 1 squared minus 1 over r 2 squared and you see then a similarity the one over R 1 squared minus 1 over r 2 squared is common and these are simply the basis of the energy either in the gravitational field or in the electric field

Channel: DrPhysicsA

Views: 193,391

Rating: 4.9160838 out of 5

Keywords: Coulomb's, law, Electric, Potential, Energy, gravitational, field

Id: GDFpTefpDME

Length: 16min 45sec (1005 seconds)

Published: Mon Mar 19 2012