You Physics and the Science Behind It

i'm gonna bring you in on a little-known secret if you open band-aids or a little bandage wrappers in the dark certain band-aids glow i am not making this up right at the bottom where the two wrappers meet as you're pulling them apart you see a thin glowing blue line and it's a really interesting little-known type of luminescence and hopefully by the end of this lesson we're gonna understand why it happens hello i'm diana cowan and welcome to lesson 18 of diana's intro physics class today is our first lesson on electricity i am of course very excited because we've talked about literally one fundamental force for this entire course and there are four fundamental forces but we've only discussed gravity so

today i finally get to talk about the electromagnetic force today's theme is secrets because i'm going to reveal the secret mechanism that your car door uses to shock the crap out of your finger i'm just kidding it's not a secret it's in a bazillion textbooks did you know that x-rays that show your broken foot at the doctor's office are the exact same phenomenon as the light shining from this flashlight that's right radio waves that carry your radio station signal the bluetooth frequencies that your wireless headphones use they are light microwaves that heat your food light infrared heat light red light all these things are the same thing and that blew my freaking mind the first time that i learned it what are they all they are all

electromagnetic waves it just so happens we can only see a small portion of the spectrum of these electromagnetic waves so now i know your next question is you know that a sound wave travels through air you know that a seismic wave in an earthquake moves through the ground so what medium does a light wave travel through you might say air but we just established that's what sound waves travel through and get this light can travel through the vacuum of space if you were a scientist in the 19th century how would you have figured out what medium light moves through you knew at the time that all other known waves traveled through some medium so you assume light should travel through a medium as well and people are calling

that medium the luminiferous ether and of course they couldn't tell you what it was but pretty much everyone was convinced that it permeated the entire universe so how could you test for it how could you test whether this all-present ether existed if nothing immediately comes to mind that's okay it's a pretty legendary experiment that finally settled it in 1887 these two guys named michelson and morley built a contraption where you bounce light waves back and forth this way and then perpendicular this way and see how the light interferes when it comes back this concept is called an interferometer and it lets you compare the path distance one wave goes versus the other because when they come back they interfere and

if say one wave went further than expected then something's happening so the idea was if earth is moving through the ether you would see some change in the speed of light along one direction as it moves through the ether wind it's kind of like if you're in a car moving along a road that like say the road is a conveyor belt and that would change the speed you're actually traveling in the car same concept fun fact this is the same technology that ligo currently uses to detect gravitational waves but back then for michaelson and morley in what was maybe the biggest failed physics experiment of all time they found nothing there was no measurable difference there was no ether this was the biggest deal because if

there was no ether then what is the medium that light traveled through the strange answer we know now is that there isn't one today we think about light not as a wave traveling in a medium but rather as get this a disturbance in something called the electromagnetic field dude what on earth is a field so the electromagnetic field is a type of force yes it's true force fields they are real in fact you're standing in a force field or i suppose you might be sitting but you're sitting in a gravitational force field i'm going to show you with some math that you already know a way to think about what fields are so take newton's equation for gravity which you already know f equals g m over r squared the gravitational force between two masses big m and little m is

gm m over r squared so let's divide both sides by little m these cancel and i get f over m equals g m over r squared equals f over m that's a from f equals m a so on earth this value f over m or gm over x squared is little g or 9.81 meters per second squared and that's true but what if we thought about this in a different way imagine putting an object some distance away from some planet like earth so i'm going to draw earth i've got a little object a distance r away from the center of earth this equation represents the gravitational force per unit mass so the force per unit mass at this point or this point is going to have some magnitude that will be equal to g times m which is the mass of earth or

whatever your planet is divided by your distance away squared and that force is a vector that's always going to be pointing toward the center of the earth it's radially symmetric and as you move further away the force per unit mass still always points toward the center of the planet but the magnitude of the force per unit mass gets smaller what i've just described is a gravitational field the field tells me that for a given mass like little m in some location at r what the gravitational force is going to be it's a vector field so it has a direction in this case every single point will point toward the center of earth but if my object is here at some distance away and say it has a mass of 10 kilograms i just

multiply the value of my field by 10 kilograms and boom out comes the force a field has some value everywhere and a vector has that but also a direction everywhere in physics we have all sorts of similar vector fields changing throughout space these fields also usually have some sort of symmetry often a radial symmetry like this and actually it's not just two-dimensional it's radially symmetric around a sphere and you guessed it the electromagnetic field is one of these radial vector fields just as a mass produces a gravitational field an electric charge produces an electromagnetic vector field the electromagnetic field describes the electromagnetic force per unit charge throughout space this means we need to

talk about electric charges you probably know that there are two types of charges where opposite charges attract and like charges repel and ever since benjamin franklin in the 18th century we called the two types of electric charges positive and negative so this would be the field for an electron which has the opposite charge so the arrows point in opposite direction it is by the way completely arbitrary that we call protons positive and electrons negative we just do it because that's what ben did so we now describe electric charges using the s-i unit called the coulomb so the charge on the proton pretty random number wouldn't expect you to guess it off the top of your head but for a positive charge proton it is 1.6 times 10

to the minus 19 coulombs the electron is much smaller so it must be a lot smaller right no the electron charge is exactly the opposite of the proton charge it's negative 1.6 times 10 to the minus 19 coulombs this is so weird the electron is an elementary particle meaning that it can't be broken down anymore whereas the proton is made up of three quarks they're two very different objects but it just so happens they have the same exact charge so how many electrons are protons in one coulomb of charge turns out you would need 6.3 times 10 to the 18 protons or 6.3 times 10 to the 18 electrons to get one coulomb so that gives you some scale why so big well because when they were defining the si units in the late 19th century they

didn't know about protons and electrons so today we can actually manipulate single protons and single electrons but back then they were dealing with huge amounts of charge so now we have to work with coulombs for the same reason that chemists are stuck with moles what is that like 10 to the 23 something like that sorry chemist we feel you solidarity so cool limbs in charge they'll push and pull each other and we have a tool for calculating how big that force is just like newton's law of gravitation but for electric charges instead of masses so our friend mr charles augustine coulomb the guy that the electric charge is named after gave us something called coulomb's law so it is f equals k big q little q over r squared force

between any two charged objects is proportional to their charges q and q and inversely proportional to the square of their distances r squared and with a proportionality constant k has a value of 9 times 10 whoops to the ninth newton meters squared per coulomb this looks a whole lot like newton's law of gravitation yeah they're both radial fields but it's interesting that they both are linearly proportional to the charge or the masses and inversely proportional to the radius squared i don't know interesting to me that this looks so much like gravity moving on so we can use coulomb's law to calculate the force between a proton and electron so we'll we'll make the distance appropriately small let's put the proton

a nanometer away from the electron so my radius is going to be 10 to the minus 9 meters away so this distance is about 20 times further away than the electron and the proton are in the ground state of hydrogen atom which is known as the bohr radius so the force in this case is going to be my k so 9 times 10 to the ninth newton meters squared per coulomb squared times my two charges and they're the same magnitude so i'm just going to square it and remember to add a negative so i'll put the negative in front 1.6 times 10 to the minus 19 coulombs and then over my distance squared my 10 to the minus 9 meters squared if i do all this math i end up with negative 2.3 times 10 to the minus 10th newtons this is the force exerted back and forth proton on

electron on proton when they are one nanometer apart that is about a fifth of a nano newton it is incredibly small but remember the mass of a proton and electron are also incredibly small what i want to actually do right now is calculate the force of gravity between the two charges so my proton mass of proton is 1.7 times 10 to the minus 27 kilograms and the electron mass is about a thousand times lighter at 9.1 times 10 to the minus 31 kilograms so if we compare this electric force to the gravitational force between them we would get force of gravity is g which is 6.67 times 10 to the minus 11 newton meters squared per kilogram squared times my mm my mass of the proton times the mass of electron

plug these in to minus meters squared all these calculations and i get 1.0 times 10 to the minus 49 newtons that is way smaller that is a tiny gravitational pull i wanted to point out something on our force calculation notice that we put a negative sign in one of the charges because the electron has a negative charge which means that the force is negative so that negative sign means that this is an attractive force which totally makes sense because we know opposite charges attract if we had done the same calculation but the charges were identical like two protons then the electric force would be the exact same magnitude but it would be positive meaning that it would be a repulsive force this is the big difference between

the electromagnetic force and gravity is always attractive under normal circumstances whereas the electromagnetic force can be positive or negative so it can be attractive or repulsive i said under normal circumstances for gravity always being attractive because there's actually some hypothetical situations in which you get a repulsive form of gravity in the early universe there's this theorized period of time where the universe expanded at this insane rate of expansion called cosmic inflation that's what the period of time was called and it's theorized that this inflation was caused by a repulsive form of gravity crazy we can apply all these ideas to talk about the electromagnetic fields generated by

charged objects so if i asked you now to tell me about some electromagnetic fields you could do it right and by tell me i mean describe them using math yeah okay i'll help you but first let me show you a fun little demo to get us in the mood so when you weren't looking i stuck some tape here on the wall of our magic science space bus 3000 and i'm going to pull it off okay you can do this too by sticking tape to the walls of your space bus or to some plastic once you rip the tape off of the plastic they will repel each other i don't know if you can see that but i'm trying to make the bottom touch and it will not ah so what i did was make an electromagnetic field on this tape and it's repelling the charges on this tape

and vice versa field on this tape and it's repelling the charges on this tape that's pretty cool but this is pretty hard to model so what about modeling the electromagnetic field of a proton just like with gravity above where we divide it out by the little m we're gonna start with coulomb's law which you now know is f equals k over r squared and we're going to divide both sides by q to get the force per unit charge so we're going to get f over the little q this is like my unit charge and i'm going to get k big q over r squared this is my electric field for the proton it looks like the one we drew before but the field is going to be repulsive by default which is the opposite of gravity

which is attractive by default so if i put another positively charged object in this field it will feel a force radially away from the proton the further away i move that charge from the proton the smaller the force gets by one over the radius squared so if i put a negative charge in here the sine of the force is going to flip and that charge feels an attractive force this is what we mean by the electromagnetic field more specifically this is the electric field we haven't included any magnetism yet but the electric field tells us how much force a charge would feel at a particular location r twice as much charge in there so you increase q and you get twice as much force so if we want to be fancy the

electric field is a vector representation of the force per charge that a charge would feel when put near another charge got it great so besides a single proton another classic example of an electric field is actually quite close to the tape demo that we did because it involves two conducting plates where charges can accumulate that's actually what i did with the tape i when i ripped it off the plastic i actually ripped electrons off the wall and the tape became negatively charged so then the negative charges on both strips of tape repelled each other which reminds me of an excellent joke so one atom says to another i've lost an electron and the second atom says are you sure the first atom replies i'm positive

okay so two conducting plates some distance apart they could be two sheets of tin foil or two metal sheets these are real objects you could really do this so we attach a battery to these two sheets one end to the positive side of the battery and one end to the negative side then what's gonna happen well on the negative side a lot of electrons are gonna pile up on the sheet and so you're gonna get a bunch of negative charges and on the positive side the electrons are gonna leave behind some lonely protons so we're gonna get a bunch of lonely protons giving an imbalance of charge more negative over here more positive over here so now we have an imbalance of charge with electrons on one side protons in the other and each proton is going to have

an electric field radiating out like this and each electron because it's negative is going to have the same kind of field but opposite where it's going inward towards the charges so what ends up happening is that all of the sideways pointing fields cancel and so you end up getting this field that's actually all in one direction and now we're in here do you think the field is the strongest say a b or c it is a trick question they are all the same strength electric field except at the edges over here where the plates end you get a constant electric field between the two charged plates typically when you do this kind of electrically charged plate problems you have plates that are a lot longer than

the distance between them so you can ignore the edges so no matter where you put another charge in between the two plates it's gonna feel the exact same force if you get further away from the protons well you get closer to the electrons so the protons are pushing if you're a positive charge and the electrons are attracting or pulling if you're a positive charge so it all balances out so you get this constant electric field in here all going this direction which means that if i throw an electron in here it'll go that way if i throw a proton in here it's going to go that way so this setup is actually something you probably have hundreds of in your pocket right now it's a super common electronics

component called a capacitor and it's one of the fundamental electrical components of modern electrical technology so your phone very likely has hundreds of them along with resistors and transistors so let's stick a little electron in here and see what happens well it's going to be pushed as we established before which means that it won't just move it's going to accelerate because it feels a constant force so say we measure the force on that electron which would be really hard to do i don't know maybe you can think about an experimental setup to figure out the force on an electron but say we measure and we know that the force on the electron is 7.0 times 10 to the minus 14 newtons so from that we can figure out the electric field strength

inside this capacitor so what is it what's the electric field strength well before we did the radial electric field f over q equals k q over r squared but this isn't radial anymore this is a constant linear electric field but i can use the same constant f over q equals my electric field i'm just going to call it e and this is another model e this electric field can be any type of field it can be radial we could just have it be a constant and that means it's linear it could be all types of crazy geometries but right now it's constant so to find e i'm just going to divide the force 7.0 times 10 to the minus 14 newtons by my charge and what charge am i going to use let me use the charge of the electron because that's what i put in there an

electron and you know the charge of the electron is negative 1.6 times 10 to the minus 19 coulombs i get negative 4.4 times 10 to the 5 newtons per coulomb and the units of the electric field or you can use volts per meter whole new unit now the volt something we're going to get to a little bit more next lesson so about 4.4 times 10 minus 5 newtons per coulomb what strength does that correspond to well if it were about 10 times stronger then it would be a strong enough electric field that you would actually get a spark through the air if this were sitting in the air typically we think of these capacitors as being in a vacuum because air actually affects the electric field but imagine i had an electric field that strong across air

the electrons would be pulled so strongly toward the positive side they would get they would jump across the air and that's actually what happens with the band-aid that i talked about the very beginning of all this when you're pulling apart those pieces you create such a big charge imbalance positive charges building up on one side negative charges building up on the other side such a strong charge of balance that electrons jump across through the air and when that happens you see a spark that's what a spark is so now we understand why band-aids glow maybe not all of it but enough so that's the electric field i know that we didn't talk much about magnetic fields but they

are very closely related and we didn't get a chance here to go in depth but they're two sides of the same fundamental force coin and in fact there are great resources out there that i suggest you search for that teach you how the magnetic field is actually the electric field kind of in a different reference frame i didn't learn any of that until i got to relativity in college but anyway we started this video talking about electromagnetic waves so how do you create waves in the electromagnetic field well this animation shows you how what we have here is a radio station on one side so basically an antenna and then some distance away you have a house with another radio antenna what happens is the radio station is basically just jiggling electrons up and down in a

metal wire so it's an alternating current if you will so you can see when the electron jiggles the electric field changes so sometime later the electron in the other antenna that one also starts to jiggle why because it's feeling the force field change the electrons are responding to that change in the electric field and if you watch the amplitude of the electromagnetic field carefully you see that the electric field is oscillating like a wave through space and you can see the electron and the antenna responding to that oscillating electric field there it is this is the electromagnetic wave that we spent this entire video building towards that wave is light and that my friends is today's lesson on electromagnetism

when they asked what you learned on youtube today here are your two key takeaways number one the electromagnetic force between two objects is proportional to their charges and inversely proportional to the square of the distance between them f equals k q over r squared and number two light is a wave in the electromagnetic field and light carries the information that charges have accelerated and don't forget to go practice these problems here are all the problems we did in today's lesson go do them on your own because that is the best way to learn physics actually to learn most things and now here's something super cool something related to light and einstein and relativity which i talked about early experiments about the nature of light also led to two other

really famous insights from einstein in which was that the failure of physicists to find any evidence for the ether gave credence to the mind-bending idea of special relativity crazy kinds of physics at the same time einstein proposed the idea that light is not just a wave disturbing the electromagnetic field it can also be seen as a particle called the photon which i mentioned earlier and now we know that all sorts of fields are associated with particles like the higgs boson which is the particle associated with the higgs field and was one of the biggest discoveries of the century discovered in 2012 or the yet undiscovered graviton the particle associated with the gravitational field we've never confirmed that the graviton exists because we can't measure it since

the gravitational field is so weak but you never know maybe someone who builds an interferometer the size of the solar system will do it could be you and if you continue on with physics which i certainly hope you do you could study physics like that and now for a message for you from a special guest hi i'm vanessa from the youtube channel braincraft and this is a message for all of the beautiful physics nerds who are watching diana's intro to ap physics course i've learned a lot i hope you're learning a lot and i have one more thing to share with you which is that i actually studied at science at university it was super fun and it has led to all kinds of unimaginably cool things that i have done in my life since

i graduated i have taught astronomy in papua new guinea and all around australia i actually worked as an astronomy tours manager so as a science tour guide in the tourism industry and every night i got paid to look up at a blanket of stars in the australian outback night sky use all kinds of big telescopes and show planets deep sky nebulae and all kinds of cosmic phenomena to the guests that we're staying at this resort it was super cool and it goes to show that there are all kinds of jobs that you can't even imagine in stem i did that i've done a bunch of other things and now i am a youtuber so there you go i hope you have learned a lot from everything because you know what learning is fun i love it and i love you too