Lecture 24 Faraday's Law and Lenz' Law

all right welcome back hope you guys had a good Thanksgiving break anybody eat too much turkey all right all right get anybody still eating too much turkey all right so I'm from the south so when I go home for an exam gets down to it to Atlanta and in in the south it doesn't count as Thanksgiving unless there's a pecan pie around and I don't know if you've ever seen how you make pecan pie you take your two pecans and you add some sugar and then you melt that sugar into sugar and then you add some sugar it's yeah all right you've had one okay so anyway I had my pecan pie as we call it the South pecan pie all right there's an error in your text that I need to let you know about oh I guess I should also tell you you may have noticed that I also caught a cold while traveling so my voice is going to be kind of weak today so I'll just ask your cooperation and keeping the background noise to a minimum that means try not to chat to your neighbor unless you can do it silently all right yeah sign language is okay all right so there's an error in your text now it's in the context of talking about the direction of changing magnetic fields so we're entering chapter 23 it's going to be about the effects of changing magnetic fields and I just want to alert you if you haven't already seen this this error in your text you'll see there's a place that says from this form you can see that the direction of DV by DT is the same as the direction of minus Delta B that's not right these guys are actually in the same direction so Delta B is in the same direction as DB when you convert it into derivative so this is what it should read there should be a minus sign there and always remember that Delta whatever Delta is Delta is always final minus initial Delta's final minus initial so if you didn't get to that part in the text yet keep in mind is a minus sign error there all right last time we talked about Gauss's law and the magnetic Gauss's law and amperes law now Gallus is law alright I should skip forward to the equations and show you galsses law here for electricity told us that if I take a closed surface all right I have to remind you of switch modes between a closed surface and an open surface has anybody ever played played with bubbles as a kid like you know it gets a little bubble on and you blow the bubbles out okay that tells you the difference between open surfaces and closed surfaces you like this and you make the bubbles the bubbles are closed surfaces okay when you dip the wand into the bubble solution and you just have the film on the wand that's an open surface a closed surface is something that has an inside and an outside a bubble has an inside and an outside when you dip the wand then you just get a soap film there's no inside or outside it's just a it's because it's an open surface okay so guesses laws about closed surfaces and it told us that if I take any closed surface like a bubble and I measure the net electric field poking through that surface and add that all up times the area involved I get a total electric flux that tells me how much charge is enclosed inside that bubble that was Gauss's law we also talked about Gauss's law for magnetism Gauss's law for magnetism looks similar on the left hand side okay the left-hand side was this flux integral right we took a closed surface that's what the circle means on the integral it means take a closed surface to get closed surface measures the electric field perpendicular to that surface everywhere and added that up times the area okay we can do the same thing for magnetic field take another closed surface circle means closed surface and add up the magnetic field poking through that and we always found it with zero which was kind of disappointing but what it means is that we don't have any magnetic charges okay so we have electric charges all right but there's no such thing as a magnetic charge at least not that we found yet remember I have a my friend dr. Bob was searching for a magnetic monopole never found one maybe you will okay so if you found a magnetic monopole we'd have to update this but for now no one's ever found one and Gauss's law for magnetism says that the net magnetic flux through a closed surface is zero so far the rest of the equations as well so the equations we're talking about our Maxwell's equations so set of four equations that tell you everything you could possibly need to know about electric fields and magnetic fields so four equations and so far this is what we know this is for the case of stationary States okay so this is this is four shouldn't say stationary States I'm sorry steady state this is the steady state situation so this is these are correct and complete for the case where any net charge is stationary and not moving and if you have a current if you have a net current that current is not changing in time so the key to these equations so far is that you might notice if you look at them and I'm I'm a theorist so I like to look at equations guys in the back your conversation is distracting to me so just switch the sign language or texting each other or writing notes okay all right so the four equations here if we stare at them and you look you will not see the symbol P right there's no time in there yet okay so these equations so far are for the steady state situation currents not changing with time charge is not changing with time nothing's basically moving alright so these guys aren't changing with time I know you guys like to flirt you're in class but you're distracting okay all right okay so no time dependence that's this case guys serious you don't have to be here okay you don't so if you can't stop talking to each other then you either need to move or leave the classroom okay thank you appreciate that all right so another time the Senate's here now we're going to start adding time to finish okay that's what we're going to be doing in this lecture and in the next lecture we'll see that there's this way to add time dependence to this equation and there's a way to add time to print it to this equation and we'll update those guys okay now what I want you to think about first before we add the time dependence is what what these integrals physically mean so we have here two different kinds of integrals right so some of these integrals are about flux and some of these integrals are about circulation girl so these guys up here about flux so I have electric field flux and I have magnetic field flux all these integrals you'll notice have closed symbols on them so if it's about a surface integral to closed surface if it's a line integral that Y dot DL or the B dot DL those are about closed loops and it needs to come back on itself okay so closed surfaces and closed loop sets with the circles mean now the top two equations are about if you have a case where there's an inward or outward pointing field so the top guide is about the case where I have say a point charge and the point charge makes an electric field that comes out from itself and those electric field lines play away from each other sometimes we call it a divergent that's an outward pointing field or if it's a negative charges in inward pointing field so Gauss's law captures that idea that if I have a net flux through a closed surface that means I have an outward pointing field okay or I have an inward pointing field and it means that I put the bubble around the center of that Ember to out reporting field these guys at the bottom those two are about curling fields so the electric field one is about takes in line integral of electric field around a closed loop all right and it tells you okay is there a circulation there or not this guy you're familiar with already in this case if I drive a current so let me have a current going through a wire then the magnetic field of that current makes is in loops fin little circles or swirls the magnetic field lines swirl around and this this line integral here captures that swirl enos so if you have a net B integral B dot DL around a closed loop it tells you that that magnetic field lines are swirling around so these guys are about curly fields these guys are about inward outward pointing field so these are the considerations we want to think about whenever you see those fluxes the net flux through a closed surface tells you you have an out reporting field or an inward pointing field it's this configuration just like the point charge if I have a circulation which is this integral line integral of B dot DL around a closed loop tells you about the circulations be around that closed loop so that's about curly fields or swirls going on all right so we take integral B dot DL and that tells us about the current that's enclosed in that loop and so right here I have for example a long wire with current coming out on the board that red dot has current coming out of the board and you know that the magnetic field lines make concentric circles around that they're swirling okay so close line integrals are about swirling fields or curly fields closed surface integrals are about poking fields they're poking out or they're poking in so I know how to get these in these cases I get a point charge gives me an outward electric field a current a line current gives me a swirling magnetic field so so far we know how to get the inward outward electric field and the swirling magnetic field okay there's something really interesting here in that the inward outward field configuration versus swirling those are actually orthogonal okay orthogonal you've seen this idea before of orthogonal you know the components of your vector different components of a vector R of za g''l to each other right so you're used to that from Cartesian coordinates where the X component is independent of the Y component and motion along X and motion along Y can be broken down and is just separate phenomena in the same way that x and y are independent Cartesian coordinates the coordinates R and theta are independent in cylindrical coordinates right so here for example if I have an outward pointing field it's Direction is away from the source right and that's an independent coordinate from this guy the magnetic field of the long wire had its direction is theta hat so it's in the sweet hat direction which is around the center these were actually orthogonal field configurations so it means that basically for any field configuration you can give me I can break up any complicated field configuration you give me I can express it in terms of inward and outward pointing fields plus swirling fields okay plus there's actually one more configuration I've missed can you can you think of one field configuration that can't be captured by inward outward or swirling around okay so there's yeah all right we got it in the back here okay yeah so basically the constant case yeah yeah absolutely I met merit high five so if you have a constant feel to the electric could be magnetic but if I say for example if you down in the back like this take the field line to just have them run straight up and have them be constant okay so if I have a constant electric field everywhere in space and it's all pointing the same direction it is neither inward outward nor is it curling okay but if I take those three ideas together the constant field plus the idea of inward outward pointing fields plus the idea of curling fields now any configuration you give me I can break down into those three components okay it's like they're independent field configurations okay now what I'd like to think about though is how can we create the reverse right so we have an inward outward pointing electric field can we make a magnetic field that points inward or outward all right well what's one way to do it what's one way to make an out reporting magnetic field my friend dr. Bob found his magnetic monopole would be an outward pointing magnetic field from it so we actually don't know how to do it because no one's found a magnetic monopole what about this case so so we have a curling magnetic field can we make an electric field that looks like that that curls around hmm okay so what's what's one of the paradoxes you would run into if you did that what if you had a curling electric field what would happen then to the line integral of e dot DL around that closed path well K so we expect that the line integral of e dot DL are on a closed path of zero because what we've done so far is relate the line integral of e dot DL to potential differences right and so we've said okay line integral of e dot DL is minus the voltage and so that tells me something it's like we always related potential to height we said anytime I go a closed loop a closed hiking path always come back to the same altitude right so if I get a circulating electric field it's going to violate that alright so it turns out turns out that there is going to be a way to do it it's just that in those cases where we make a circulating electric field we're going to have to be very careful with that potential equals height analogy is what's going to happen all right okay so let's see if using all this great physics equipment we can come up with some curly electric field all right mm-hmm all right I'm doing this because I don't like physics equipment okay so what we have here is some solenoid all right this guy right here is a solenoid that I can't hook up I can turn off so make sure not okay when it's on the light bulb will go the light bulb is just to show you yes there's current running through this circuit so it's current running through the bulb just to show you it's on and then current runs through this big long solenoid a solenoid is several sets of concentric well of circular wire loops and the point of that guys to make a magnetic field right this is an electromagnet it's rather big electromagnet but it's an electromagnet so when I turn the current on like that there's a magnetic field poking out coming back in and there's a very strong magnetic field through the center and then when I turn it off there's not right now this guy is separate from this this is also kind of like a solenoid except it's not hooked up to a power source okay so this is several turns of wire and then it took tup to this guy which is not a power source it's actually just yes okay it's actually just going to measure 4's current okay so basically a fixed coil will there ever get current through it this needle would deflect so I'm going to turn this guy on remember when I turn this guy on there's a strong magnetic field pointing out of its top but it's just a big magnet all right so we push this over here and there was a little transient there did you see that okay I'm going to pull back out okay and again there's a little transient that happens okay so it's a little bit bigger effect if I actually turn it on or off so when I turn it on or the big effect when I turn it off there's a big effect okay on off alright so there's something going on in this guy this guy can tell even though it's it's not hooked up to a power source this guy can tell whether or not this guy is hmm is doing what can it tell us this guy's on okay it's on are you getting a reading that says it's on yeah pardon it can tell if it's changing right so right now I've got it on but there's no deflection but if I change it there's a response if I change it there's a response so this guy can tell if the magnetic field coming out of this solenoid is changing or not okay if it's constant it's no big it's not picking it up so somehow this guy knows and if this guy knows right it's because it's got current running through it well how would it have current running through it if the only way to drive that current would be Affairs an electric field that's pushing the current around those wires right and in this configuration that would mean there'd have to be a curling electric field so we just figured out how to make a curling electric field okay the answer is change something okay and the thing that we're changing in this case is the magnetic field so if I change the magnetic field poking through these wires there's a curling electric field that happens as a result you have any questions so far okay all right and this is a really fun demo I can find there's the ring okay hmm so what I have here is a bunch of turns of wire that's just an electromagnet down here you can see lots and lots of big thick copper wires and they're about ten deep it's about 300 turns of wire and this is just an aluminum ring the aluminum ring will carry current if if there's a curling electric field through it okay so what's kind of fun here is that I've got it situated so it's centered right on top of the solenoid and when I turn the solenoid on this guy is going to feel a changing electric field I'm sorry a changing magnetic field through it and in response to that changing magnetic field it should do exactly what this guy did it should have a curling electric field drive some current through the ring right you ready to see it okay I love this demo ready all right so something happened it's always fun to see you again all right that that was cool all right got another ring here all right bad ring the first ring again okay that's more like it all right so there's something going on and I need somebody in the front row to examine the Rings for us and tell them it's the difference okay the bad the bad loop okay has a flaw which is that it's not closed so this little gap over here in the ring that didn't work so what's going on is that as we turn on the electromagnet down here okay so we'll turn that on real quick all right as that happened with the changing magnetic flux through this ring okay and then there was a curling electric field right the curling electric field drove current because it's a ring this guy experienced all the same stuff so when we turned on the magnet it had a changing magnetic flux through it drove a curling electric field yet there's a gap here so it couldn't carry current all that happened was that it shifted charges a little bit charges built up at the edge and it was stuck right so this guy is the one that's font so just do it again because it's fun now what do you think's pushing it up this guy didn't quite do that right so something's pushing this guy up yeah there's a magnetic force on it okay so the magnetic force is that we know our QV cross B that's one of them okay or if you take QV cubes for a point charge right but if I take many many many point charges inside of a material I turn that QV and the IDL so inside of this hunk of material the force is going to be IDL cross B so what's going on is that as I turn the magnetic field on this guy gets current running through it well there's current which means I can have an i DL cross B okay so if I take currents over this way I crossed into well there's a magnetic field coming straight up okay so I crust into view this way is this going to give me an inward radial force that's not going to do anything except tend to either contract or expand the ring so I have to actually consider the fringe field so the Frick shield coming out of the solenoid comes up and splays out so think of that splaying component so now I get I crust into the outward pointing magnetic field that's going to give me this guy right that's going to be what drives it away it turns out that a ring will fly away from either side of the solenoid just like that which is fun and yeah okay you can see this smoking I love this I just want to get it where you can see it all right this is liquid nitrogen all right so we like liquid nitrogen right notice I am wearing protective eye covering so if I take the ring and soak it in the liquid nitrogen you know term icon that catching that it's boiling right because I stuck a warm ring inside of it sweet for to stop boiling maybe so what I'm doing is I'm I'm torturing the poor little aluminum ring okay but also I'm cooling it okay what what happens to the conductivity of the ring as I cool it yeah okay so the resistivity goes down as I quit right but the conductivity will go up so this guy now that it's cold hopefully so it works now that it's cold it should carry a lot more current what do you think's going to happen if it carries a lot more current yeah you guys watch out okay doc if you need to stop duck alright don't pick it up thank you you guys okay no students were harmed in the making of this okay lecture yes that was cool huh okay so the point of showing you that was that remember when we talked about how the resistivity changes as a function of temperature now you've seen it yourself right when it's cool it does you want to see it again I can tell like Chris talked and just dip the ring it again okay sure pick up that cell that's liquid nitrogen boiling all right all right ready I I don't want to catch it so you guys just watch out okay and don't touch the ring oh good it came back outside all right good job ring all right everybody give a hand to the ring because it's been through quite through another day alright good job little ring so okay that was a lot of physics but back to our point okay our point is that we found out that we can make curly electric cables okay we just did it in a couple of different ways well it's all the same way right we're taking a changing magnetic fields a changing magnetic field causes a curling electric field so what what we do is we're changing the magnetic flux through that ring touch what's going on so we're going to have to update our Maxwell equations these are Maxwell's equations with no time dependence there's no T on that slide okay I'm question sorry yes oh I see okay okay so the question is is it really fair to say that the electric field is curling isn't it just a loop that's curling so the reason I know the electric is be careful images of the reason I know the electric field is also curling is because to carry a net current through this loop would require is an electric field here driving current and an electric field here driving current and electric fields out here driving current and so forth all the way around the loop so I'd have to get an electric field all the way around the loop that fits in a circle so so while the currents going there has to be a curling electric field inside that that wire yeah that helped good good question other other questions good question all right so so so what that what that really means is that when I turn the solenoid on there are curly electric field down here no matter what if there's a ring there the ring will run current so there's not a ring there there's still a curling electric field okay that helped some okay good good questions thank you hmm so we gotta update this so because we just figured out that we can make one so that's not always zero if there's a time-dependent okay for the flux the magnetic flux that's changed with time so there's a D by DT change the time of magnetic flux then we can cause a curling electric field so now I need to tell you a little bit more about what that math means so far on the left-hand side all the integrals have circles on them which means if it's a surface integral two closed surface like a soap bubble okay if it's a line integral two closed loop like a track that you would run on or something like that this guy on the right does not have a circle and that's on purpose so what that's about is if I have a ring okay so so the case you need to analyze is we have this curling electric field which is the current Vale a line integral of e dot DL around this closed loop the circle of integral means closed loop is equal to minus D by DT integral V dot NDA but we have to define the area of that loop okay I'm sorry we have to define the area of the flux on the right hand side so here's how you define the area of the flux take this Lu oops dip it in the bubble solution and the film of the bubble that's the area over which you need to calculate this so whatever your line integral is on the Left write your line integral to find the path could be circled like this could be a crazy loop of something or other all right dip that structure in the bubble solution and get a soap film that soap film tells you this area on the right side you have to calculate the flux to now because it's a soap film and not a bubble there's no inside or outside it's not a closed surface that's an open surface okay so I don't have the circle on it Jenny any questions about how those are late right the guy on the left is like your bubble wand right the guy on the right is the soap film on the bubble wand questions alright so we updated this one so far all right now we still have more to do next week we're going to correct this guy and we'll see that next week there's actually a way to also make a contribution from changing electric fluxes as well that'll be that'll be next week then once we have all those pieces together then that will be the entire story that'll be everything there is possibly to know about electricity and magnetism alright so let me go back to something we've done before but now I want to interpret it in terms of Faraday's law so Faraday's law was this guy that if I take the line integral of e dot DL around a closed loop that's equal to minus D by DT of the magnetic flux through the soap film associated with that loop so that's Faraday's law now we've seen this before this was a case that we analyzed by a different equation but it's the same physics so let me just remind you what we did before and then we'll interpret it in terms of the new Faraday's law that we learned today so we've always had this equation forces QV cross P write F is QV crusty or in the context of a material the QV of a point particle turns into IDL inside of a material so here I have the setup where I have two rods that are conducting I have a resistor connecting them and I have this bar that's that's also connected to both rods and the bar is something that can back and forth and I have a magnetic field these blue X's are magnetic field poking into the board the X's are like the arrows on the tail feathers on an arrow so these magnetic fields that way and now if I reach in and grab this bar it's actually hard to do if I grab the bar and try to pull it it's hard you remember when we did B as the generator demonstration and we saw that if we turn the hand crank we could run an LED bulb fairly easily but we had to work really hard to run an incandescent light bulb so it really is hard to be moving wires through magnetic fields okay that's the difficult thing so in this case here I'm going to reach in grab that wire pull it through the magnetic field and at first before I touch anything there's actually no current anywhere right before I touch it nothing's going on I grab the bar strip moving the bar now all those charges inside the bar feel the force equals QV cross B right so then the electrons are moving with a particular velocity as I move the bar then there's that V crossed into B drives a force this way all right and then I get a current going so now that I'm pulling the bar now there's a current now the current goes into this resistor where the energy dissipates that's why it's so hard to pull this thing I try to pull it and I'm burning energy through the resistor as I do it okay so we did this before and we analyze it in terms of forces QV cross B all right that's what started that current moving but I can also interpret in terms of this equation okay can you find how as I grab this bar and pull the bar to the right can you tell me what would happen to this equation yeah yeah it increases so I've got this set up so that the magnetic field is constant but as I grab the bar and pull the bar to the right the area through that loop will change and that's what this guy's about so the line integral of e dot DL through that closed loop depends on minus D by DT of integral B dot NB a where a is defined by the loop itself so if the loop gets bigger its area gets bigger and this area gets bigger it's the flux is changing so I drive correct so it's what you've learned before but now in terms of Faraday's law we have a different way to look at it okay same physics different language you have a question about that any questions okay all right here's another case we've seen before that we can also think of in terms of Faraday's law so if I move if I move a magnet into or out of a loop of wire I get some current running so actually have a demo about that let me turn that on okay so this is just a big well several turns of wire okay so this is several turns of wire here and here it will tell us if we have current running through the wires but okay all right if I hold everything steady there's nothing interesting all right and this is a magnet okay so if I move the magnets around I get stuff going on okay all right so basically this magnet done as I move it around causes currents to flow which is that situation so I can also think about that in terms of Faraday's law right in this case the area is not changing so what's the piece of the magnetic flux that's changing if the area is not changing it's the strength of the magnetic field that goes through I think of this of a soap bubble over this the soap bubble then I need to think about magnetic field poking through the soap bubble and that's changing as I as I move the magnet in or out okay all right now the other thing we should figure out is all right I'll hold it still now watch which way the needle deflects as I move the magnet towards it okay okay it deflected to the right now I'm going to pull it out and it deflected to the left so it goes in at the flux to the right goes out it deflects to the left so that's contained in the equations here because the direction that this is talking about well I'll have to have to show you the right-hand rule but there's a right-hand rule associated with how you relate the vectors of that integral here of a line and it will round the loop to to the flux through the surface but suffice it to say that there is a connection and I'll show you that soon it tells you which direction that current was going to run right have any questions so far right here's something else kind of cool so what's that needle and North is roughly that way okay so I should be getting a pretty good flux of Earth's magnetic field through here so watch this I don't want to want to move the wires going to hold the wires still okay sometimes I wave this around I'm changing the flux of Earth's magnetic field through the loop and you can see that can you guys see in the back Vanille responding okay alright so there you go another another way to detect your magnetic field if you're without a compass and yet you have one of these little volt meters okay yeah okay don't do that alright q have any questions so far all right all right so both of those can be summed up as the Faraday's law there's another way to write Faraday's law which is that we can talk about your question here okay all right so there's another way to write Faraday's law versus Faraday's law but I can also say that this a dot DL is like EMF right the EMF driving the current through a circuit and this flux I've just made up a new symbol here okay since this is flux magnetic flux Greek symbol Phi v stands for stands for flux okay so we use Phi to denote that flux and then you can write this law in a slightly smaller form but they're the same thing so when you see this it's that okay so it's basically telling you EMF around the loop is equal to minus V buddy - you have a magnetic flux through up through the through the soap film that would cover that loop question so far okay definitely time for an iclicker question all right hmm so get out your iclickers warm up your clicker fingers so here's the setup I got to tell you the setup because it's a little bit that's not terribly clear from the diagram so I'm going to have two cases up here of an infinite solenoid so this is not a solenoid but pretend it was a solenoid okay so pretend it had coils going all the way around it right so the magnetic fields coming out of coils of wire is very strong inside and then if there's an end of the solenoid the magnetic field has to loop back around but imagine making an infinite solenoid right so if I make this infinite of both sides and yet I'm running current all the way through it then I'll get magnetic field inside but if there's no end of the solenoid there's no place for the French field to come out so for an infinite solenoid okay which we have to incident solenoids up here here the circle represents a solenoid this circle represents a solenoid and this is the sense of the current so B is pointing out okay so in both of these cases there's an infinite solenoid like this and there's a magnetic field pointing out towards you and it's increasing so basically we're turning up the cards on this incident solenoid right so and then we have loops of wire the big thick lines are loops of wire so here's the loop of wire all right and here's another loop of wire and they're complicated but what I want you to think about is EMF around the loop of wire based on changing magnetic flux through the wire so there there is this set up okay which one of those two loops will have currents in it all of them neither of them or it's only one which one all right so tell me what you're thinking what do we need to think about to analyze this problem yeah thanks you okay so you're arguing that there's no currents on either one because yes okay all right so so here's to uh this is very I'm glad you brought this up okay so he's saying look outside that solenoid there's no magnetic field okay nothing touching this wire no magnetic field touches the wire how in the world could the wire possibly now right so wire can't respond excellent line of reasoning all right you're shaking your head do you want to what's it what's is there a counter-argument to that because that's a really good argument okay that wire is touching no magnetic field very weird all right is there a counter-argument that what's the flux how do I talk like the net flux through the wire all right now you don't have to be intimidated by his line of reasoning there's there are more stuff to think about this is a really solid line of reasoning but there's more stuff to think about so how about the flux how much like the flux yeah okay all right so okay so the first line of reasoning got us set there shouldn't be anything because neither of these wires is touching a magnetic field how could it possibly know yet the equation we have says that it's about the flux through through the loop and so in this case I do have some flux in here right so this there is flux in here is I think that's what you're saying there's in here but it's not through the loop of the wire so doesn't count right so here if I go through the entire loop of Wired I go okay every place you know think of a soap film on that wire okay so is the soap film intersecting magnetic field no no no no no not in here not in here not in here but in here it is and here the soap film is going to cut through some magnetic field lines and any place that silk film cuts through some magnetic field lines that gives me a contribution of the flux and then as that magnetic field changes I get a contribution of flux so you're arguing that by golly I know the wire is not touching the magnetic field how can it possibly know and yet this imaginary soap film is touching the magnetic field lines and it feels the flux increase in there must be a response okay this is what this is a classic paradox okay because the two lines of reason they are getting us different different answers so the answer is all right and then again it's a paradox the answer is that if we if we do the actual experiment though we will see that the guy on the right actually has current running through it so even though that wire doesn't touch the magnetic field it's imaginary soap film would touch the magnetic field and it would have changing flux through the slits through the soap film and yeah I see people throwing their brows because this is really weird and so if you have some deep questions about locality of physics come talk to me after class okay and I'll tell you the resolution to that because it is it is a really a deep issue but it is also true that this is the case that has changing magnetic flux to it so we have to conclude that this guy would have some current running through it as you change the flux okay it's a bit spooky right action at a distance kind of thing and yet it works so the answer here is C okay and I'm glad we brought up both sides because this is actually really surprising but the answer C and the difference the difference is basically if I have a loop so pretend this for my infinite solenoid okay so pretend I have some wire on an infinite solenoid and then this represents a solenoid that's now busted through both walls and it's gone to infinity if that were the case I have no way to get this ring off right can't take it that way that's intimate can't take it that way Tintin it's stuck okay so it doesn't really matter right there's there's any configuration it has it's always going to have the same flux through it so it will always have that response now if I did this though and now I make the solenoid infinite now there's no way to get the ring on so it'll never have a flux through it in that case all right so very weird spooky action at a distance and yet to get action at a distance here so the answer C to C all right so again this was Faraday's law it told us that if I have a closed if I have a closed loop no matter what shape then the EMF EMF is defined as the the closed line integral of e dot DL okay same thing that EMF then it can be caused by changing magnetic flux through the soap film okay so any sheep wire dip it in bubble solution it makes a soap film if there's any magnetic field lines poking that imaginary soap film which is here then if there's any change in that magnetic flux you'll get an EMF alright questions about that okay now I need to tell you the direction so let me skip ahead a little bit and tell you the direction of the curling field right what we saw before was that there is a definite direction to this thing right so when I had this Weaver wire and I brought the magnetic magnet toward it it deflected one way when it pulled the magnet away it deflected the other way so we need to figure out if increasing flux drives current this way or if increasing flux drives it that way all right so here's how to figure that out and look at the top left example all right and this is a place where in the text of your book it had a little sign error so that let that confuse you that was my announcement that on the first slide right on the top left example here what we have is we have magnetic field pointing out toward you and not going to feel going to be pointing out toward you it increasing so it's going up question is which way does the which way does the curling electric field go through here's how you can look at it B is increasing this way point your right thumb in the other direction and then your fingers curl in the direction of the curling electric field okay so magnetic fields come out this way and increasing so Delta B is out toward you Delta B is positive okay but I have to point my fingers the other direction flip them over minus DV by DT is n to the page and my fingers curl around in the direction of the curling electric field okay that is the right hand rule I went through that a little bit fast because personally I think this is confusing all right you're going to get practice with this on your homework but let me tell you in my opinion an easier way to remember it okay so here's the easier way to remember it okay if you've learnt if you've learned lenses rule before then you know how this should go if you had a loop of wire present okay remember whether or not the loop of wire is present there's still a curly electric field there okay so what I want to talk about is think about this magnetic field increasing out towards you but I'm going to put a loop of wire around it okay the loop of wire lenses rule is that the loop of wire tends to oppose changes in the magnetic flux to it so think of the loop of the wire and the soap film over it and the flux through that soap film it doesn't like changes in it so it tends to oppose it so the loop of wire will spontaneously generate some current so as to oppose that change okay so let's think how that would go so magnetic fields out toward you and increasing alright the wire here lenses law would tend to oppose that change if I run a current this direction okay if currents going that direction and I point my thumb along the current then the magnetic field would be pointing in magnetic field that the wire generates so the wire tends to make a magnetic field that opposes changes in its flux that's I think that's a quicker way to remember all this if you know lenses law and then the direction of that current has to be the same as the direction of the curling electric field okay Jeff any questions about that either way you want to work it out is fine and we'll get you the same answer I just find this one easier to remember than that one okay all right and we're done for today see you on Wednesday

Channel: Prof. Carlson

Views: 1,987

Rating: 4.891892 out of 5

Keywords: Physics 272, Physics, Electricity, Magnetism, Matter and Interactions, Faraday, Lenz

Id: BlPctmU1VUg

Length: 44min 18sec (2658 seconds)

Published: Sat Jul 29 2017