Lecture 20 Electricity vs. Magnetism; Rail Gun

all right welcome back last time we talked about the Hall effect and one of the things that we learned was that in some metals and in some semiconductors current is actually carried by the absence of electrons which is kind of weird what we mean by that is that if you have an electron C and you have the kind of situation where it looks not so much like the electrons C is flowing by but the main thing that you see is bubbles and the electrons C going by then you may as well address the problem in terms of holes holes are like bubbles in the electrons C and you know there's some situations where that's not a useful idea if we make the analogy with water then water coming out of a water hose you want to think of a water you don't want to think of the absence of water coming into the hose but in the case of the Acme bubble o matic here putting air bubbles through the fish tank you didn't really want to analyze that in terms of the back flow of the water around the bubbles it was easier to track the bubbles right so sometimes it's useful to think in terms of those holes okay and the Hall effect was something you could use in order to tell inside your material was it mainly carried was the current mainly carried by electrons what was the occur intended by bolts so many questions from last time here's the question if I have a proton moving with this velocity to the right and there's an applied magnetic field into the board I just want you to coming back here this is Monday morning coming back after the weekend just want you to figure out which direction does the the force the magnetic force points for that proton okay and there's your equation there so first answer you're on your own and then it'll give you time to talk to your neighbor with almost 150 votes in tell me tell me what you thinking who who would like to Monday morning kind of remind us how this goes yes please Thanks oh okay - you want to tell us okay okay all right so he's saying right hand rule you can find your right hand right so right hand and I say the velocity is pointing this way the magnetic field is into the board so I curved my fingers that way and then my thumb points up in some people actually that the first lecture so you know there's at 8:30 lecture in a 9:30 lecture the 8:30 lecture taught me a new trick that I hadn't really used myself and they said look point your put your index finger along V and then your second finger along B and then your thumb points up along the force okay so in both cases we get that it's up now do it for an electron okay so same situation same magnetic field same velocity but now it's an electron which weight is a point to this direction in this case all right overwhelmingly you're all getting the same answer so anybody want to walk us through how to do it this kind this time you're volunteering or evil entering him okay all right so we take the velocities this direction and then curl the fingers into the magnetic field we would have gotten up but it's an electron so we just have to switch the sign because of it the charge on the electron or whew heresy okay so somebody up front mm-hmm will remain nameless Alex putting it out that you could use the left hand rule for electrons right I didn't get your name wrong today okay good so you can't you can I prefer not to I prefer to put that sign in efforts but if you know how to do that and if you know that you're not gonna mess it up but you're going to only use the left hand rule the unauthorized version for electrons yes totally works you're totally right all right any other questions okay so that was to get us thinking along the right lines because we'd like to be thinking about this in the context of a hunk of material okay so now we're going to take a hunk of material in the shape of a bar let this be a conductive material so let's say a metal bar and we have a magnetic field pointed into the board and we just want to take that bar and pull it okay so you're just gonna make that bar move at a constant velocity and we want to see what's going to happen to it all right so so the bar is moving at a constant velocity it's the same situation that you just calculated there are electrons inside the bar that are free to move because inside of a metal the electrons we say that the electrons are part of the electrons see because they're fluid they're liquid they're they're free to move around and so they can move and when they feel this magnetic force as you all calculated downward then electrons will start moving all right no question is though I'm just gonna keep moving this bar along we're just gonna walk with this thing it's like walking it on we're just gonna walk it for a while all right in this magnetic field the whole time it's got this magnetic force on it all right as you point it out the right-hand rule says these electrons are gonna tend to go downward but how far is that gonna last I'm gonna I'm just gonna keep pulling the bar at constant speed will I get a current forever in here maybe maybe what'll happen is that we just invented a new weapon and as we drag this thing along the electrons just keep moving and we just start shooting electrons out the bottom lots of good grins on that one but probably not gonna happen right so what happens the electrons reach the end of the bar and then no way yeah I'm not gonna get constant-current right if this is a free bar I'm not gonna get constant current this is very much like and and this event is coming up so you better be mentally prepared for it but this is very much like all of us outside of the doors at BestBuy before it opens the Friday after Thanksgiving right so the crowd comes up to the to the doors and they can get to the doors but they can't get in so the crowd comment pushes against but the doors aren't open that's the best by the day after Thanksgiving and you get stuck so here at the bottom the electrons just kind of pile up all right so they'll pile up and then they'll exert forces on each other due to the pileup right so we'll get nut charges gathering down here a little few electrons gathering at the bottom there'll be some exposed positive charge at the top so when the electrons see shifts down there'll be a little bit of exposed atomic cores at the top now please don't think that their bare atomic cores you know protons just dangling off the end it's just that the electrons see shifts a little bit relative to the atomic cores exposing some positive charge at the top and negative charge at the bottom so charge builds up and as the charge builds up then I get a voltage due to that and then there's an electric field that counteracts all this motion so in the steady state right I'll pull this bar across yes there's a magnetic field that pushes the electrons down but then as the electrons build up they exert a force back on the ones that are trying to come in and then I get net well I get a steady-state situation okay so in steady state the charge will build up until there's an electric field that balances all this stuff out all right and so then in the steady state the net force on the electrons will be the electric force plus the magnetic force so the magnetic force we already talked about was QV cross B the electric force QE I don't know what the electric field is but here's how we can calculate it right you know one way we could think about the electric field as well if I knew the pattern of charges down here I could calculate it that way but that's the hard way the easy way is to know that well the charge is just gonna build up until I have no net force on this thing right that's because electrons are liquid inside of a conductor if there is a force on them they will move and so they will move until there's no net force the time scale on this by the way is about a picosecond electrons are really really fast so this will happen until I get no net force so that means this term must balance that term the V and the B are at right angles okay so then the magnitude of this guy is QV B so it must balance out the electric field there and in steady state the charges will just arrange themselves so that there's a net electric field in the bar that's opposing all this motion all right so that'll be our steady state case in this situation right - have any questions about that okay so there's something a bit odd here and then I have a steady-state situation of a conductor and I've got an electric field inside of it are you okay with that okay up until now we've we've tended to say that the steady-state situation inside of a conductor was that the nuts you know that okay so we basically just got a balance going on right so we've got a balance going on its steady state it's alright okay so now all right we thought about this we said okay the electrons aren't going to shoot out the bottom bummer we would have liked to have seen that but if we connected the thing up to a circuit we could actually use it to do something so let's do that let's connect it up to a circuit so now I've got the same situation I've got a bar in a magnetic field that's going into the board we're going to move the bar along again at constant velocity but this time I've got the bar on Rails okay so it's electrically connected two conductors above and below and then there's a there's a resistor that's connecting those bars so I make a complete circuit here but the path of current is going to change as I move the bar alright and everything's metal except for the resistor so same situation I'm going to move the thing along and I still have this force right so here's the hand that's going to push this thing along and as I do this I still get a force downward on the electrons all right but what happens to the electrons now when they get to the bottom of the bar are they going to get piled up again like the previous case okay right they just keep going in this case so this is like all of us outside the doors our best buy the day after Thanksgiving and now the door is open okay so there's an electrical connection here so the electrons can just flow on through and we get electrons moving clockwise we know the conventional current goes in the opposite direction so conventional current goes counterclockwise so I can think though about well okay I could use this to get something right I could use this to drive a circuit element like a resistor or maybe a light bulb if you actually wanted to do something useful and I can think about well how much work are we going to have to do in order to keep this bar moving at constant velocity okay you might think well maybe once the transients are gone right maybe once I just get the thing going and just kind of push it maybe I can just let go and it'll keep going all right but there's there's something fishy with the energy conservation in that all right because we need to think through that all the forces that are on the bar so when I'm in order to keep a constant velocity on this thing I actually have to fight something the thing we have to fight is that once there's a current established in the bar that current now means that that there's another force on the bar all right so I could think of we could think first in terms of electrons at first I'm pushing the bar along so I'm moving electrons across magnetic field lines but then the electrons start moving down as well so now there's this downward component to their velocity that downward component to their velocity causes another force and that's a force due to the magnetic field so you can see it in the equations here so f is QV cross B the magnetic force on a charged particle in the context of a current carrying wire we take the single particle QV and turn it into I Delta L so in the context of the current carrying wire this becomes I Delta L cross B so as soon as I set up a constant current situation now there's this current with a crossed magnetic field okay I Delta L cross B so I have another another force involved so it's not just the force that my hand puts on the bar but there's the force that the magnetic field is exerting on the bar as well question probably I have to look up how I'd have to look up how a railgun works but yes you can you can totally use these concepts if you would like to use these concepts to make projectiles at high velocities you can tonight that's what you're really getting at is can we use this to build the gun yes you can yeah the railgun fires a projectile faster farther and with greater impact than a gun that uses gunpowder where a 5-inch conventional gun can send a projectile 13 nautical miles the Navy says the railgun consented 110 nautical miles Chief of Naval Research Rear Admiral matt winter said he expects the railgun will be on navy warships in the next decade it's like a flux capacitor right you're sitting there thinking about these next generation and futuristic ideas and we've got scientists who have designed these things and it's coming to life see trials begin in 2016 made possible since researchers reduce the amount of space the gun needs yeah don't try that at home okay or if you do don't tell my cold yeah okay so we've got the the current moving along there's a force backwards on the bar and in steady state those two forces must balance right so to keep this bar moving because the current then makes them you know because of the current the magnetic field exerts a force back on the bar I have to fight in order to keep this bar going fight just means I'm going to keep putting a force on there so it's this situation you've already seen when I run current through these wires they get attracted to each other remember we saw there's two cases either the currents parallel this is the parallel current case and they get attracted or the currents in opposite directions and they get repelled it's a little harder to see the case of repelling but there it is okay so when they're attracted to each other it's pretty clear and I managed to do it with no smoke coming off the terminals II yet so I smell smoke though so I can calculate in this oh so similar things were going on here right there was a current in the presence of a crossed magnetic field and the magnetic field exerted a force on the wire so same thing here that's what the hand has to fight is that force from a magnetic field so we can calculate then well how much work am I gonna have to do how much power am I gonna have to put into this thing in order to keep it moving so to keep the bar moving at constant velocity I'm fighting that that force from the magnetic field which as we said is AI Delta L cross B and it's got to be equal and opposite to the force of the hand and the magnitude of that is ilb okay why did I skip the sine theta skip sine theta yeah exactly everything's at right angles here and sine of a right angle sine of 90 degrees is 1 so I'll be so the work that I have to do okay the work that the hand does is going to be the force dotted into the distance and they're parallel in this case so I just get F Delta X so the magnitude of the force is ILB times some distance Delta X that I move it over but I'm gonna keep moving it okay I'm gonna keep moving it so as I do that I have to put in a certain amount of work per time in order to keep this going so work for time is power it's the definition of power is energy per unit time so I have to put in that amount of work per unit time which is ILB Delta x over delta T once I see a delta x over delta T I should think in terms of a speed or velocity so we'll write this down as a speed il be V and that's the work well that's the power energy per unit time that I have to put in to keep this going alright now I can also then recast this this is really close to a familiar equation once I say the power is current times something that should look familiar okay power is current times a voltage drop right the power in an element in a circuit is current times the voltage across that element so this must be a voltage alright and we can see that that actually is a voltage so let me show you how that is so the voltage across this bar or if you want to think of it as EMF you can there's an electric field in here right there's an electric field in the bar and so the electric field in the bar we already calculated is magnitude of V times magnitude of B in steady state and then to get the total voltage drop across the bar I just multiplied that electric field by the distance so if L is the length of the bar and by L here we mean length of the current path right not the total length of this bar but the length that goes from one rail to the other rail all right so that's this L here so VB L and that's the the voltage drop across it actually your muff it's the voltage increase across it the power then is I times this EMF which matches I Delta V okay as we would expect do have any questions about how that all went okay so to keep that going now you can use this to do useful things okay this basic concept of taking a wire and moving it in a magnetic field right we just generated power okay didn't use it to do anything particularly useful in fact where's all my energy going right where is it ultimately going yeah it goes into the resistor so I'm putting work in by the hand okay I'm converting it to electrical energy which think goes into the resistor and turns into what ultimately heat right that's what resistors do they basically whatever energy gets some 10 of them goes out as heat and the way that that happens of course is that there's electrons running through the resistor the resistor is one of those materials that has there's a lot of collisions between the electrons and the material so fan bam-bam-bam-bam these electrons are just whacking into the atoms in there and as they do that they dump all their energy into the atoms inside the resistor again and again and again and again and they're doing it at such a high rate that basically that's where all the power gets dissipated in this kind of setup and ultimately those energy transfers to the lattice when I say lattice I mean the regular arrangement of atoms inside the resistor the you know you dump energy into one atom it kind of Wiggles it makes its neighbor wiggle and so forth to keep these little waves inside the crystal waves those waves you get enough motion that basically it gets just turned into heat okay if you want to ask me more details about the head go ahead after after class we'll have to get into thermodynamics and things but basically it's something to heat so if we wanted to use to do something useful we could have run a light bulb alright there's something else useful you can do with it if the slides will advance no slides advancing for me today don't know why alright so here's something useful you can use it for energy harvesting right this is one technique for energy harvesting does anybody happen to have an energy harvesting something okay there's a lot of ways to energy harvest some some watches actually use this principle for energy harvesting they'll have a little have a magnet and they'll have a little wire that can run back and forth near the magnet and then you capture the electrical currents they get generated as you do that some other it's much more common if you have an energy harvesting watch it's much more common for it to be mechanical actually so there's kind of a little heavy ball that rolls back and forth as you move your arm around and that ends up winding up a spring but you could also have the electrical kind of energy harvesting it's used in some watches and you can use it other places as well so you can use this to do cool stuff any questions so far okay all right time to settle the age-old question again who would win in a fight we answered this before for electricity and gravity but now it's time to pick magnetism versus electricity so this is just a vote just an opinion poll I know we just finished election season and I'm taking an opinion poll but full credit for any answer you give who do you think would win in a fight magnetism versus electricity it's a no-holds-barred fight battle of the forces who's stronger all right the opinions are still rolling in but would you like to know the results of our completely scientific opinion poll roughly 44 or 52 slight favoring to electricity slight favor so our current projections current projections that could be that electricity whines but we should actually do the calculation okay we're going to use a cool trick to find out here's the one cool trick use this one cool trick to find out the one cool trick you need to do this calculation is it turns out I'm not going to prove this to you but you can scribble out the math yourself nu naught times epsilon naught happens to equal a very familiar face in physics the very familiar face is 1 over C squared C is the symbol we always use for the speed of light the speed of light in vacuum is C so it turns out that Mew naught times epsilon naught is 1 over C squared so these guys have been appearing in our equations so which one of these is the electric one epsilon naught okay F so not shows up in our electric equations which ones the magnetic 1 by process of elimination u naught u naught is V is the magnetic 1 so the magnetic equations have this mu naught running around the electric equations have this epsilon naught running around and it turns out when you multiply them together you get 1 over C squared so we're going to use that to to answer that so let's set things up all right let me set things up we'll set up the fair fight we'll go kind of through the electric forces and then the magnetic forces so let me have two positively charged particles let's do that mind like water thing they do in in martial arts just clear your mind then the only thing in the universe is these two positively charged particles okay number one and number two cleverly named what kind of force do they feel yeah there's a Coulomb okay there's a Coulomb repulsion on these guys and that's what we would measure okay we would measure a Coulomb repulsion so that there's a there's a force equals QE on these guys each one exerts an electric field to the pot each positively charged particle exerts an electric field on in space the other charged particle feels that electric field and then there's a force do you have any questions about that so far so it's definitely the electric field No I'm going to move them okay let's have them move relative to us at constant velocity and so we watch these two positively charged particles moving by we know they have this electric force between them now is there magnetism involved now okay all right why I'm hearing some noise I'm hearing some yeses so yeah okay so the velocity causes a magnetism to happen right so so a charged particle just by itself exerts an electric field if the thing is moving then we also observe a magnetic field as present okay so they're moving so they're both causing magnetic fields to happen so there must be a QV crust B as well they still have this electrical force and now there's going to be a magnetic force between them and in fact you've already seen it with with the wires right when we run the current you're gonna run it in the parallel case there's an attraction there okay so these guys are going to have something very similar happen as well all right so to remind you of the the magnetic part this this demo here we already figured out before we could think in terms of current going parallel we said when we had two wires with parallel current I could think in terms of one wire on the other what are the forces between these guys so we broke it up into this is from the last lecture lecture 19 so I have cards in the red wire current in the blue wire and the red wire exerts we're gonna call it a red magnetic field okay I can use the right hand rule for that current goes this way magnetic field is coming out towards you up here and the blue wire feels that then we have the I Delta L cross B that the the blue wire feels so the blue wire has a current going this direction I crossed into the B is coming out to you guys and then the force went downward on the blue wire and then equal and opposite meant these guys were attracted to each other so that's this demo here and that's a very similar situation right so here I have current going to the right here I have two protons going to the right okay so two positively charged particles moving to the right very similar to what we already thought of and so there should be that magnetic attractive force between them so we'll build it up slowly though let's do the electric force first so first just think in terms of electric forces here's the total force we're going to have to consider QE + QV cross B but first electricity then let me just zoom in on particle 2 so I'm going to think of the the first particle particle 1 okay a positively charged particle it exerts an electric field in space as it's moving it also exerts a magnetic field in space and I'm going to think about the effect on particle 2 so particle 2 feels this electric field what's the electric field due to particle 1 it's 1 over 4 PI epsilon naught Q 1 over R squared times our hat and then the electric force on particle 2 is it feels that field and then multiplied by its charge that tells you that the net force on particle 2 so the force on 2 is Q 2 times u 1 multiplying those guys together I have the 1 over 4 pie epsilon-not all the Q's here are of magnitude e we're setting it up that way so I have an e squared then over R squared and that's the electric force and it's repulsive since they're the same same sign of the charge so it's it's downward do you have any questions about that one so far ok so there's a repulsive electric force that was no surprise ok there's a magnetic force so let's calculate that and then we're gonna let these guys Duke it out and see which one wins so we have a magnetic field again thinking along the same lines I want to calculate the effects on particle two ok so particle 1 puts out its electric field because particle one's moving it also puts out a magnetic field and that magnetic field due to the moving particle one is Mew naught over 4 PI Q on V one cross R hat over R squared okay so then the magnetic force on two actually I should tell you which direction that goes but it's the same as this double wire experiment so I have this positively charged particle going this direction I need to then calculate V cross R hat ok so here's I need to figure out which direction this magnetic field goes in for this positively charged particle if we go back to the biot-savart law which has the V cross R hat our points to me right so I always put myself at the observation point so I'm going to have the observation point be here at particle to our points to me so our points from particle 1 down to our observation point so that tells me then V cross our hat goes that way and then the magnetic field is pointing back into the board right there okay so step 1 is where is that magnetic field pointing back into the board does that make sense you could also have thought of it as okay this is a positively charged particle and I can think of terms of current put my thumb along the current and then my fingers curl in the direction of magnetic field so there's a magnetic field at particle to do to particle one right and it's pointing into the board so now this guy are the force on it because it's a charged particle moving through a magnetic field that's crossed to its path so I'll have a QV cross B term so QV cross B in this case all right we've got the V crossed into B right so I put my hand in the direction of V or it's probably clear if I just do that the fingers so V is the index finger then B is back into the board and then the force is going to be up so the magnetic force up on this guy here's the magnitudes right I take the magnetic field magnetic field had a Mew naught over 4pi there it is the Q is of magnitude II there's one power of velocity there's another power velocity here okay and then another power of charge and then it's all over R squared so all together we got Mew naught over 4 pi e squared V squared over R squared why did I use the same symbol for v1 and v2 yeah it's just the way we set up the problem that's all it is ok I've set up the problem such that these are both moving at the same velocity V okay so that's why V is appearing here twice really it's a v1 times of e2 okay so there's our net of the net magnetic force that we observe we have to remember of course as soon as we say velocities are involved we have to be real clear that this is relative to the frame so the lab frame is us we've got those positively charged particles moving by a velocity V relative to us the observers and that's the view that goes into that equation so there's the magnetic force do you have questions on that so far okay the main thing that I want you to get out of this is that the magnetic force depends not only on you not but also in that velocity okay all right so putting them together so so now let's let's compare who would win in a fight I have the electric force in this corner and now the magnetic force in this corner so the electric force on particle two we already calculated was 1 over 4 PI epsilon naught e squared over R squared times R hat the magnetic force on particle 2 we already calculated it's magnitude was mu naught over 4 pi e squared V squared over R squared so if I just look at these forces the similarities okay are that there's an e squared in both there's a 1 over R squared in both there's even a 1 over 4 pi in both so now I just want to take the ratio right we'll use this one cool trick that Mew naught times epsilon naught is 1 over C squared and now when I take the ratio of these forces say okay take the magnetic force divided by the electric force so here's the magnetic force we already calculated it it's Mew naught over 4 pi e squared V squared over R squared now divided by the magnitude of the electric force it's a squared over 4 PI epsilon naught R squared so now when I look at these equations what's going to cancel well I have an e squared will cancel that u squared I have a 1 over R squared in both cases and it's the same R so those cancel the 4 PI's cancel then left would I have am you not there's them you not this epsilon naught is a 1 over epsilon naught in the denominator so it comes back up to the numerator epsilon naught and then there's the V squared so I get altogether the ratio of forces is mu naught epsilon naught V squared okay and then we use the one cool trick the one cool trick is mu naught times epsilon naught is 1 over C squared and I can okay now we always know that particles don't move faster than the speed of light okay so C is the speed of light in vacuum nothing's allowed to go faster than that so I know then that whatever these speeds are they're gonna be less than or possibly equal to but less than the speed of light okay turns out if it's a particle that has mass it's always going to be stuck at less than the speed of light so we can always say that this magnetic force is going to be less so that answers the question it was electricity who won okay so electricity ends up being bigger do you have any questions about how the calculation went or any of that what's that ratio in a typical circuit okay so we're gonna have that the ratio of the magnetic field to the sorry the magnetic force to the electric force is V squared over C squared I'm reminding you of the drift velocity inside of a typical circuit is about three times ten to the minus five meters per second okay do you remember the speed of light are you needed me to tell you I'll put it up it's three times 10 to the 8 meters per second speed of light whose brave brave enough to volunteer their neighbor to answer the question oh right here Oh your volunteer your neighbor thank you oh he's like I'm not sitting by you guys next time all right okay okay all right so he's squared on both and then took the ratio so he said look the drift velocities 10 to the minus 5 all the units are gonna cancel out the threes are gonna cancel out I set it up that way so it's 10 to the negative 5 squared is 10 then I get a 10 10 to the 8th squared is 10 to the 16 so I'm gonna get a ton and the 16 and I get all together 10 to the 1 is 26 okay thank you for being for bravely volunteering your neighbor to answer the question okay kudos so all right I need to take V over C squared here V we said was 3 times 10 to the minus 5 meters per second C was 3 times 10 to the 8 meters per second got a square it always remember squaring the 3 is cancel the meters per seconds cancel inside the parentheses I have the 10 to the minus 5 10 to the eights in the denominator so it comes back up as a minus 8 I still got a square it 5 Plus 8 can you give me a 13 there squared and then I get a 10 to the minus twenty six so that's pretty extreme right it means that the electric field is 10 to the 26th of the electric that force the electric forces were calculating it's 10 to the 26 times larger in this case that's one with 26 zeros after it which is approximately yeah gajillion okay it's a lot right so how do i reconcile that with this experiment okay I am clearly observing a magnetic force right you're clearly observing a magnetic force and yet that magnetic force is somehow down by twenty six orders of magnitude from electrical forces so can you reconcile it in this what's the resolution yes please okay so there's the number of electrons playing in definitely I have a lot in here so anytime good point anytime I have a hunk of matter that I can hold in my hand I'm just gonna estimate that it's roughly a mole maybe 10 moles but a mole has about 10 to the 23 particles in it so there's a lot in here so it could be that there's just a magnitude difference yes okay could be oh the angle so in our set up I should put the setup back up good ideas all right let's this is a good brainstorm I should put this brainstorm back up so maybe it's okay what are the codes so the thoughts were maybe it's maybe it's the number of electrons electrons and that's that's large that's like 10 to the 23 and hunk of matter and you said maybe use the angles let me put the setup back up so our setup for this fight is here and I have positively charged particles going parallel to each other so actually the angles are the same what about what about in our constant current situation here right what's the net electric force between these two wires okay how are you getting zero what uh yeah I mean the thing is that inside this material right actually this has the current going the same direction right but inside the material I have the same number I do have about 10 to the 23 electrons and I have about 10 to the 23 protons as well and so they balance right this thing is a net neutral object and this is a net neutral object so the electric forces between these guys have already been haha don't say canceled out but but basically a net neutral object has he's not going to exert a net electric force on anything else so the electric force here you know it's the same situation we saw with with gravity the electric force is really really really strong okay they blew away gravity and it's blowing away magnetism it's just that it's such a strong force that all the matter that we touch has already had the electrons and protons get close enough to each other to form atoms and then you have a net neutral object so that's why we're not experiencing these tremendously strong electric forces we actually are experiencing in them and the fact that they they make up our entire body right in the form of the atoms and the molecules so that's why we didn't experience it in the in the case of of this guy right here it's net neutral so net neutral net neutral meant that there was no net electric force on these guys and all that was left to observe then was the magnetic force but we F we had just had this situation of two bare charged particles traveling together the main thing we would have seen is that they would just fly apart from each other and we would barely notice that there's a little bit of a shift right what we saw was that either this calculation tells you that if I go back then to calculate if I calculate the net force right if I were to add these guys up doesn't even matter that the magnetic force is opposed to the electric force in this case it's down by 26 orders of magnitude have you ever written out of calculation with that many decimal places in it I mean have you ever had that many sing you would have to have 26 significant figures in your calculation in order to care about this so who cares right no we care that's why we're talking about it okay so now there's something really cool that we're getting very close to which is relativity so yeah wait this should be cries of roading okay so uh well let's think about a different situation let's just run alongside these oh I called them electrons but they're really positively charged particles so sorry alongside these positively charged particles and let's just rather than measuring them from our lab frame and they're moving by let's send one of us okay send one volunteer to just run alongside them okay we're gonna run alongside them and as you run alongside them at the same speed that they're running at what are you the runner measure as their velocity relative to you did you catch that we're gonna take one one volunteer anybody want to volunteer and run alongside them yes what's your name Cory okay so Cory's gonna run alongside him he's gonna run really fast cuz he's a really good runner he's gonna run alongside them at the exact same speed as them so Cory measures that they're at zero speed they have zero relative speed to you okay so you're not gonna measure any magnetic forces in his frame of reference okay so as long as he's moving at a constant velocity he is what we call an inertial reference frame he's a valid you are authorized to do experiments on behalf of the physics world if you're moving at a constant velocity okay that's called an inertial reference frame so in here's a nurse'll reference frame where he's running at exactly the same speed as these guys he measures zero magnetic field and zero magnetic force so there's something Wiggy going on here all right it actually turns out that relativity is coming up in this because we're having to to get to understand the full physics here we're having to talk about relative velocities right and that should clue us in that one of the things we need to think about is relativity itself so we all right what you need to know for relativity is this thing called gamma is going to make our lives easier so let me introduce for you kind of one of the main characters in relativity so relativity here's a strange thing about relativity it sparked a lot of philosophy of course you know philosophers got wind of what was going on in physics and the physicists said well it's all relative but in fact we shouldn't have named this thing relativity okay we should have named it constants because what relativity really says is that the speed of light is constant in any inertial reference frame so C is constant equals 3 times 10 to the 8th meters per second no matter what always always always always always okay so relativity is really a theory of constants so should be called theory of C equals constant no matter what okay so if C is constant no matter what that means that even if we send Corey to go chasing a photon right photons travel at speed light Cory was our runner before I'm gonna send him to chase the photon now he's never gonna catch up no matter how good a runner he is because he as long as he's moving at a constant velocity he's a valid inertial reference frame if you're in a valid inertial reference frame moving at constant velocity you're authorized to make measurements on behalf of the physics world and then you will always measure that the speed of light is the speed of light even when you start running at 90 percent of the speed of light or 99 percent of the speed of light you'll still measure that so relativity basically says that things warp how do I say this you things warp in order to preserve the speed of light so basically how is this possible space but I can't spell space this is why I use powerpoints okay space and time warp I kid you not to preserve the speed of light all right so space and time warp to preserve speed of light and in fact they warp in in ways that that we know okay we had to do experiments and calculations to figure this out but how these guys going to warp think they warp in these ways basically when things start moving at close to the speed of light when V gets near these things we get what's called a length contraction length contracts time dilates I told you space in time would warp right and even masses mass is going to increase and we'll see you next time bye how much all right gotta let you go cuz we're out of time

Channel: Prof. Carlson

Views: 1,669

Rating: 4.8095236 out of 5

Keywords: iMovie, Physics 272, Phys 272, Electricity, Magnetism, Matter, Interactions, Physics, Introduction to Electricity and Magnetism

Id: -gLzdhG0IiE

Length: 44min 15sec (2655 seconds)

Published: Sun Nov 06 2016