#physics , #apphysics , #magnetism
review mass spectrometer, magnetron and LC circuit, cyclotron and use in medical field/ LHC video. Hall effect. E vs B for a charged particle. Biot_Savart law. magnetic field for a straight wire. force between two straight wires.
Okay so do remember we have a test so I increase the window because someone had work so now it’s from 8 to midnight but uh don’t forget to take it because otherwise you’ll have to come the day after at 8:00 a.m. in person okay so make sure you don’t miss the
Test number three test number three is going to cover only no it’s going to cover some some um circuit okay like the equivalent resistance and the maybe um voltage divider for example aren’t you happy that you came early today so you’re going to have two problems on
That and it’s going to be conceptually heavy and it’s going to be covering unit five so a lot of conceptual questions so don’t don’t forget your right hand okay for test number three make sure it’s working so remember for negative charge you can use your left hand right hand is
Positive charge and to help you I have this uh slides in addition to the regular slides with everything that I try to summarize because I know that electromagnetism is not so much about the math at this level it’s it’s about concept okay so talking about about
These slides here um if you have a moving so it has to be moving and it has to be a charge and the charge needs to have a velocity at least one component of the Velocity perpendicular to be so in that case it will be acted upon by a
Magnetic force that force will be a centripetal force so that Force cannot accelerate the charge it can only making go um curve make make it curve okay so again you use your fingers here so if it’s a if it’s a positive charge positive charge for you is this way
Magnetic field is in the screen the force will be this way so you have a circular motion in this direction and if it’s a negative charge it’s going to go in the other direction so this is a circular uniform motion uniform because the speed does not change okay Mass spectrometer very
Important if you go work in a lab chemistry or even biology so the way it works you take a bunch of Isotopes for example and they don’t have the same mass like neon has different isotopes or nickel and then you have to make it into
A gas and then you have to to ionize them so you can hiip them off of one electron so they all have one Elementary charge okay one one e 1 1.6 * 10 the 19 Kum so they will be all positive charge so all those isotop will
Have the same charge and they don’t have the same mass and then you use um you apply your voltage to get them to move right so it’s they they will get an they will be acted upon by an electric field the electric field will accelerate there and you have potential energy turning
Into kinetic energy right so Q is the charge U is the voltage that will be kinetic energy and then they are supposed to have all the same velocity but you all have done statistics especially for biology or chemistry or even engineering statistics is very important so they they will have a
Distribution of velocity even though it’s supposed to be the same it won’t right there will be a distribution so we need to have them with the same velocity so we use a velocity selector so we apply at the same time a magnetic field and an electric field and you see for a
Given velocity on only one specific velocity the electric force of course it’s going to be down but it will be balanced out by the magnetic force you see the velocity of the charge going this way the magnetic field is in the screen so the magnetic force is up so
For a given value only a given value of the Velocity do we have up equals down so you have the Velocity here will be equals e over B okay so that b here usually is not the same as this B so you use two magnetic field one electric
Field here of course a voltage that you apply there so then all those Isotopes they’re going to enter that magnetic field here with exactly the same velocity they’re going to have the same uh Q Mass uh charge sorry they will be inside the same magnetic
Field so the only thing that Set uh set them apart will be their Mass so that way okay you can move up and down detector and here you can collect the the less massive one will make a sharp turn the more massive like a larger term okay so you can detect those Isotopes
You can find the mass of isotop and you can find you know the abundance okay so how many isotop 22 how many isotop 21 how many isops 20 if we are talking about a neon this setup was developed by JJ Thompson 1913 and that’s how he was able to find
If you look here you you see you can isolate Mass over Q okay so he found for electrons so he discovered the electrons and he found for the electron the ratio between its mass and the charge okay using this equation okay and it was also used during World War II during the Manhattan
Project when they were working on the atomic bomb you have a physicist named Ernest lawence that use this idea to enrich Ur because if you have uranium 235 uranium 238 you see uranium 235 will be curved more than uranium 238 but you have to do it over and over it’s not
Very efficient method but was the first method use and then they use other like centri okay so that’s just the review that was for the pop quiz you see that’s a setup with a CRT cathod F you can use a magnetic field that you can make with
Two coils the helmet uh Co okay so uniform magnetic field and you can use an electric field so one will bend up the other one will bend down and if you tune the magnetic field just right it’s easy to tune the magnetic field you just have to change the current uh they will
Go straight and and deflected and that’s that’s where you can find the ratio between the mass and and the charge is that clear okay then I want to go back quickly CU we don’t cover the we don’t cover our RLC or or this is a capacitor so L this is a solenoid LC
Circuit we don’t cover it but it has so many applications incl including a Tesla Coy for example so I just want to say few second so remember this this is the magnetron very very smart magnetron has cavity here so you can see that here someone took a part like a
Microwave okay so that’s where the microwaves will be produced so the electron are emitted so you need to apply a very high voltage I forgot the voltage let’s let’s cheat here oh 4,000 volt wow okay so very dangerous device here don’t don’t break them apart for for extra credits
Not worth it so there is a Step up Transformer 4,000 volt here that you are using so anyway those electron are going to band around the magnetic field that you get with a simple simple magnet and they will oscillate back and forth here and why do they oscillate because this
Here is called the tank circuit okay it’s like o or resonant cavity so it’s a tank circuit because this will behave like that circuit here when you have a capacitor and a solenoid so this is called the LC circuit so the electron will be forced to oscillate and you are
At resonance so the frequency will be 2.4 gigahertz which is about the same frequency as a Wi-Fi for example so you want to make sure that your microwave doesn’t cck out microwaves and I made a video just to to tell you about this uh oscillation resonance in the
Nsh I was just listening to music sorry about that so if you want to have resonance with a circuit you need the AC power supply okay you need a solenoid and you need a capacitor so the way a capacitor works it will resist the build up of charge
It will resist the build up of voltage because of course you put the first positive charge it’s fine but as you keep adding positive charge it’s going to resist because they repair each other so capacitor is like a a spring that you try to squeeze okay so you are building
Potential energy and at some point it’s not happy anymore you want to discharge okay so he wants to snap back uh soleno it we didn’t talk about that yet but that will add inertia to the motion of charge okay so it means inductor will resist the change in
Current okay it doesn’t want the current to change too fast so if it’s going too fast it will slow it down if it’s slowing down it wants to keep it going so this is like inertia this is like um a spring that you try to squeeze and you
See here you have the frequency of the power supply the frequency is 0.5 Hertz which means half a cycle per second okay so it means a cycle will be 2 second you see it’s a S Wave okay so you can see here that’s the outlet that we have here
So you have plus and it will do like this this this is plus that plus will be here then it will be here okay so it’s um it’s a sine wave it’s an AC alternating alternating voltage and you have the frequency here but that’s not the resonance frequency
So yes you have oscillation but nothing special and then you can increase the frequency so the frequency is going to increase okay so and and of course the inductor is not happy about it so it’s going to try to slow down the charge but still nothing about that the current is not very Large so you decrease the frequency okay so now the frequency is decreasing so now it’s the capacitor wants to block so the current is not very strong still but if you get to the resonance frequency it’s 022 225 actually but you see how the current is going to increase by a lot so
That’s going to be right and the the current is like 10 amps before it was 1 amp and now the PE PE current is 10 so it works exactly like like the spring and the mass okay and in electronics it’s not cannot get a a disaster but if you have a Bridge like
The Takoma bridge and the wind it was um in Washington state the wind started to push on it to push on it push on it get to Resonance and you break the bridge yeah uh is a disaster because I think Baltimore is one of the most important
Port right in in in the US maybe it’s going to be worse for us because all those boards they’re going to come to Florida because come to Miami so I don’t know if it’s good for us I think it’s incompetence but I don’t know I know do I know about okay so I
Wanted to take a parenthesis um okay so we talk about that elola okay so I keep that for the pop quiz it’s um something similar to that so what’s interesting about this motion is that the veloc has two components one component is perpendicular to B so because of that component you will have
A circular motion into the YZ plane into the YZ plane YZ plane you have a circular motion but at the same time it has a x component so at the same time that it’s going around in the YZ plane then it’s also moving forward so it’s like a flat Slinky here that you’re
Going to stretch out in this direction okay because you remember in physics I think it was Galileo who said that motion are independent from each other and they can happen at the same time they are independent from each other so it’s like the projectile motion okay okay so let’s go to
Another uh okay so here we talk about that okay so a charge wants to go around a magnetic field so this is how the Earth is protecting us from cosmic R so if you have those beautiful Van Allen bels that was discovered during the race space race between Soviet Union and the
US and the US um were the one who discovered that and then you can use that idea of partic going around the magnetic field in what it’s called a magnetic button so you see you have two coil here the magnetic field between them is not uniform so it’s going to be
Weaker here stronger there and what it will do and you can look at your book wire you can think about it it will make the particle um trapped okay it cannot Escape so that way we have a way using magnetic field we have a way way to trap
Charge particles so we have a way to trap plasma okay so it’s used a lot in the lab so you see you can you can have a plasma of course you cannot have Plasma in the bottle right so but you can use a magnetic field here so the plasma will
Be trapped around here inside that donut and here you have coil that you have to cool down by a lot so it cost a lot of money and you can use use it to build what it’s called a Tokamak Tokamak is when you have plasma okay so charge
Particles and you trying to make fusion happening they keep trying for the last 30 years but it’s still not efficient they do it but it’s not very efficient another application we talk about that okay that’s called as velocity selector there is a YouTube video If you interested here that goes over all those
Steps we talk about that we talk about about that we talk about that okay now something amazing it’s called a cyclotron so cyclotron was designed by Ernest Lawrence Ernest o Lawrence he was from berley University so again the guy who work with Oppenheimer on the Manhattan Project but
Before that he got the Nobel Prize because he he he buil the cyclotron so cyclotron it’s very smart if you want to accelerate charges right so if you want to accelerate protons it used to be that you just use a linear accelerator okay so you apply electric field and you make
The charge speed up and then once you have your linear accelerator you can have a atom smasher okay you can have them collide with each other but it takes a lot of space he got this amazing idea look what he’s doing so here you apply a voltage which is AC so the
Particle here comes out could be a proton it’s going to be deflected by the magnetic field okay now remember if we go back to the equation for circular motion you see the frequency the frequency here so the frequency will be one over the period is not velocity dependent it depends on the
Charge of the particle here it depends on the Mass on the magnetic field but not of on the velocity okay so that’s going to be very very smart it’s very smart the physic is not hard to understand but it’s super smart look at that so you apply your magnetic field going into the
Screen okay so you see magnetic field uh so the the velocity is going this way this way I mean for you will be this way magnetic field is in the screen so the force is down so it will make a curve here right you you can use a permanent magnet or
You can use Co when it’s going to reach that Gap here because you apply your voltage it’s going to speed up okay so now it’s going to go faster so because it goes faster the curve increases right the r I is going to crease and here you have a ac voltage so
The electric field will reverse you speed up curve speed up curve speed up curve and it doesn’t take much space so now you have a a projectile a proton you can use a proton as a projectile so why do you want to use protons for example
In a hospital you can have what it’s called um proton therapy for cancer so proton therapy you use proton to destroy your tumor so it’s less damaging that regular therapy radiotherapy but of course you know Insurance it depends on insurance some cover and don’t but it’s less damaging because when you have
Radiation radiation therapy the issues is that on their way to the tumor God forbid on their way to the tumor tumor they’re going to destroy those radiation will destroy healthy cells so it’s just your hope that you you’re going to have more benefit than risk I say that
Because I was teaching Nuclear Physics nuclear medicine so in nuclear medicine the first thing you learn is risk and benefit right you’re going to take some risk is it worth it so proton therapy has less risk I think I already talked about proton therapy so anyway the thing
To understand here is that you see it will always take the same time to go from here to make that half circle will always take the same time because it’s not velocity dependent so even though it’s going to speed up okay it will always take the same time so that way
You can apply your AC power supply okay all over always with the same frequency so what you are doing with the electric field you push with the magnetic field you bend you push you BN you push you BN okay yes similar to the technology used for
GMP what is oh yeah so it’s is it a radi radio isotope that you use I’m not sure educated on it but I you said projectile in terms of the yes so what is EMP electromagnetic pulse it’s supposed to disabl yes so so so the EMP if it’s a
Pulse this is a pulse okay so here you’re applying a pulse but I don’t know for therapy so in that case what you are yeah so here you have a pulse right so each time it’s go through the Gap the electric field will be be in One
Direction the other direction you p p p you push push push push but for the what is it used for is to accelerate a charge particle and how is it used so you see it takes some place so only hospitals you know big hospitals will have them
And it’s used for pet scan okay so again not always covered by Insurance you cannot have too many pet scan because when you are taking a pet scan you are highlighted from inside out by gamma rays so you you you increase your risk of course so you don’t want to have that
Too often it’s just that it gives you a great resolution if you want to see details so you see it’s called a cyron so in that case the way it works so it’s not for cancer therapy in that case you accelerate that proton right that will become a projectile and for example
You’re going to heat a nitrogen molecule which is not radioactive okay and you the the art the product here will be I isotop so what you are doing is like Alchemist you are playing The Alchemist right you are you are turning turning one ele element to another one so and
You are making radio isotope those radio isotop can be used in medicine and they have a very short life because you don’t want to go outside take the subway and you are all radioactive so after the Pet Scan they will ask you you know stay stay for a while so the radioactivity
Goes down so why do you want to make something radioactive so let’s say you are making oxygen radioactive oxygen goes to your brain let’s say that you want to see what’s going on in the brain so you’re going to mix oxygen with sugar for example in a pill you make it
Radioactive so this is radioactive half life is 2 minutes so the the peel with your radioactive oxygen and should it go to the brain because oxygen the brain loves the oxygen plus it has sugar the cancer cells what they want is to eat sugar that’s why you have to stop
The sugar if God forbid so anyway it goes to your tumor and there okay the oxygen which is radioactive it’s going to Decay and when it’s going to Decay it’s going to produce a positron okay so in inside the tumor it’s going to Decay produce a positron positron will combine
With electron and what’s happening when you have a matter and anti explode okay annihilate each other and you’re going to have a burst of energy in the form of gamma RS so you have matter anti inside the tumor you have a burst of gamma rays so conservation of momentum one goes this
Way the other one goes that way and then this way and that way and that so you are highlighted from inside from with gamma so that’s how a pet scan works right you can also make radio isotope for example if you want to detect a tumor as well so
They’re going to use radio isotop because again they will mix it with sugar and a cancer cell will ferment all it does is to ferment to to consume sugar so the sugar will go to the tumor and then it goes beep beep right because it’s radioactive
So you know where it is so that’s the idea one one of the application so you have those cyclotron here very no those this is very expensive that’s why insurance will not be happy to cover it it’s very very expensive because you you need to have a
Voltage suppli so you have to use electricity all that is very expensive and so you don’t you don’t find them in clinic you find them in the big hospitals uh it’s a good question do you see on internet how much you need for for a pet scan like a
Cyclotron they use that for the large hron collider it’s a good question I I’m it cost a lot to build and it cost a lot to run so it’s a good question I don’t know how much voltage you need several thousand wow and then and then you you need to
Have of course special lab technician that are certainly certified because you have to handle radio isotope that’s also money and then you have to hire people you know to inspector to check if you are doing the right thing so I guess it cost money yes one I I from from maybe it changed
You have don’t take it for truth I’m not sure but I heard it’s like they don’t say you should take more than one per year huh four four times in one year oh okay yeah one one per year I will say but check that out because it’s
It’s a balance right because you pet can the amazing thing is that you are using very small wave L right so you have very good details so very good resolution so you have MRI which is not very good resolution and then you have CAT scan which is a better resolution because you
Are using X-ray and then gabet have a small like the principle is that the the the size of the details that you can see has to be larger than the size of the wavelength that you are using it set a threshold so if you are using gamma ray that means you will see
Very small details because gamma have a small wavelength right so that’s why in biology you use electron electron microscope because electron waves have a small wavelength so you can see better with a microscope so if you are using an optical telescope you cannot see details smaller than the wavelength of visible
Light that’s that’s the rule so application of the cyclon insignificant though this I’m not going to show everything but that’s a it’s a accelerator so particle Smasher between Switzerland and France it’s inside the ground and that’s the idea okay you use an electric field or a voltage to speed up you use a
Magnetic field to make it spein and at some point you crash the particles together the charge particles together and that’s how they discover in 2016 the hix bosom hix bosom is the god particle the the particle that gives Mass to things so but it’s very very very expensive to run because they need
To have this strong magnetic field that they get with coal so they have to cool down the coal right and energy is like a terra terra electrovolt so 10 to the 12 electron vote so that’s how it it marks the beginning of the world’s largest and most powerful particle accelerator chain
Culminating in CERN spectacular large hrop collider hydrogen cylinder are fed at a precisely controlled rate into the source chamber of a linear accelerator cerns linac 2 where their electrons are stripped off to leave hydrogen nuclei these are protons and have a positive charge enabling them to be accelerated by an
Electric field their Journey to eventually take part in ultra high energy collisions similar to those following the Big Bang can now begin this initial acceleration has caused Lin 2 to be likened to the lumbering first stage of a huge rocket by the time this packet of protons leades Lin 2 it’ll be traveling
At 1/3 the speed of light it’s about to enter the booster stage two of the rocket if you will in order to maximize the intensity of the beam the packet is divided up into four one for each of the booster rings straight acceleration is now impractical and the booster is
Circular 157 m in circumference in order to accelerate the packets they are repeatedly circulated and the electric field is now pulsed in the same way that you push a child on a swing each time they reach a certain point magnets exert a force on the passing protons at right
Angles to their direction of motion so this is just to people for people to understand you don’t use a battery you use a power supply which is AC you don’t use a horseshoe magnet you use a coin that frequency has to be really really fast and so powerful yeah so it’s it’s
So it’s going to go faster and faster and faster ELR magnets are used to bend the beam of protons around the circle so in that case you you since it’s going faster and faster you have to change the magnetic field the booster accelerates the protons up to 91.6% of the speed of
Light and squeezes them closer together combining the packet from the four rings it’s then flung on into the proton synchrotron by analogy stage three of our rocket let’s just follow two such proton packets the cannot translate into increased velocity as they’re already approaching the limiting speed of what is interesting is that as
They go faster and faster because because of the power supply that you apply their mass is going to increase because as you get close to the speed of flight speed of flight is the maximum limit in the universe so as you get close to the speed of flight the mass is
Going to increase so that’s a special relativity so there is a limit you cannot go faster on the speed of FL light in traveling to keep so that it’s a stering magnet finally brings it to a collision course the total energy of two protons colliding in the LHC is 14 Terra
Electron volts and reproduces similar states to moans after the big Bang particle tracks from these collisions will be analyzed by computers connected to the detectors and it’s hoped these tracks will give a new insight into the very birth of our universe so they did found the higs bosone at the end so Terra 10 to the 12 so in a typical chemical reaction you
Have one electr two electr nuclear reaction it’s much more yes IE how do they ionize them no because in the mass spectrometer you do the same thing you have to ionize so how do you ionize I have to look it up I don’t know if they make it hot or I
Don’t know how it’s done but they always do that like for example in a mass spectrometer here you have to ionize so I will look it up how they make that happen so in that case it’s just simplified okay just for people to understand the main ideas but even here
You have to ionize if you want to use a mass spectrometer the Isotopes have to be ionized so I don’t know how you ionize you have to excite the electron enough that they’re going to leave the outmost layer right so you need to apply some kind of energy to excite them and
They live they break free so I will uh I will look it up how it’s done in that case Okay so Nobel Prize 1938 Ernest Lawrence so you see here how it works what it looks like how it’s used and again the idea is to use an electric
Field to accelerate my magnetic field to make it speed yeah mention that as the particle speed light massre yeah where that increases Mass comfor it’s special relativity so Einstein shows was able to show and you you show it in the lab like if relative to you okay you’re not
Moving if I was able to go really fast I will feel fine okay I cannot ose that weight that I want to lose but when you look at me you see that I have my mass will will um will have increased so that’s why you cannot go faster than the
Speed of FL because as your mass increases so that means you need to burn more energy to accelerate so if if something goes really fast the mass will increase and it has done in lab where they take particle and when they move really fast when you compute their Mass it’s going
To be less what they are supposed to be when it’s at rest okay so it’s special relativity second not only the mass increase but the time slow down so if I was able to leave the Earth go really really fast and then come back I will be
Uh you will be older than me maybe for me one year had passed and for you 20 years will have passed I I I don’t I don’t realize that because my watch seems fine but your watch says that your watch says that your time went faster
Than me the time slow down so in movie Interstellar have you seen the movie Interstellar so he goes for a warm hole so inside the warm hole the time stops so when he comes back to Earth his daughter was about to die because she she adop to be older than him not only
That the the length will contract so when you look at me if I go really fast I will be very very thin even though I feel fun so it’s very weird but you can see that you can see that in the lab so yes right so if you have a particle that
Is supposed to leave for that much time you you you see in the lab that they live for longer like some particle are not even supposed to make it to Earth but they do because their time um goes slower so when you have a GPS so GPS you have to take that in Account okay so it’s um it’s it’s weird Okay so another application here is called the whole effect and that’s what you use to find the magnetic field of to measure the magnetic field so here that’s the whole effect here you see um you you have a circuit
Power supply and if you apply a magnetic field here you’re going to move the charge so you’re going to create a voltage here that voltage here will be proportional to the magnetic field proportional to the current so it’s called the whole sensor so if you like to play with microcontroller like arino
You can buy that for a few doar right it’s called a whole sensor and you can measure the magnetic field I think that’s what you did with the with the lab okay you had like a sensor which is a whole sensor shove that into the selenoid and you were able to find the
Magnetic field this this is because of that and okay so this is a whole whole effect you can use it to measure the current or to measure the magnetic field and even the rot rotation rotation speed so if you have like a wheel spinning for those going into engineering you can attach
Like a magnet here and here you have a sensor when the magnet goes next to the sensor the the voltage will increase so by by finding the frequency of the voltage uh increasing decreasing you can find how fast the the wheel is spinning Isn’t that cool right and so electric field magnetic
Field uh so let’s go back to here so again an electric field will accelerate so in that case you can get like a projectile motion because you have the electric force in this direction so the charge wants to accelerate in this direction but at the same time it’s moving at a constant
Speed so you will have a projectile motion if you have a charge moving in a magnetic field you don’t get a parabola you get a circle it wants it wants to uh Cur around the magnetic field boom boom boom we almost done okay so remember magnetic field
Can can act can can produce a magnetic magnetic force only if the charge is moving and if you have a component perpendicular to the magnetic field okay so then we have um the Len Force so that means you can apply both an electric field and a magnetic field
So last time I show you like an app and you have a very rare motion you use that in a velocity selector Mass spectrometer you going to use both electric field and magnetic field and the cyclotron okay cyron you are pushing pushing pushing okay so summary so the summary is that a
Moving um the source for magnetism is a moving charge okay and um that’s the source for magnetism so here it comes from another book and it’s called Johnson and Cel which is good if you are taking the MCAT Johnson and cell um it’s it’s very oriented application in biology or
Medicine so anyway at the end of one chapter this chapter it has the summary here of all the equations so if it helps you you can print it out for test number three or for the final I will not repeat it just uh if you want and it has all the
Explanation here it’s a very nice summary okay so you you have most of the equation that we have used here the other one you can find it yourself so if you want to find the frequency you just say the velocity is the distance divided by the time the distance around is 2 pi
R the time is the period okay so you can find the period if you have the period you can find the frequency copy that okay so so unit six is not in test three okay so test three is just this unit and and a little bit of circuit like
The I like a voltage divider for some reason okay so just a review from the first unit so I don’t want to explain go over that again but remember we talk about field lines that’s a concept introduced by Michael F so we talk about electric field light if if you can show
That if if for example the charge here is a big charge here you going have a lot of field lines so they’re going to diverge if you have a a small q here okay you’re going to have less of them okay so we remember we talk about Gus law okay so Gus law
Says that if you take a imaginary imaginary surface closed surface okay the number of field lines poking through that Clos surface will depends on the charge that was G slope the number of field lines is just a way to comprehend what’s happening you don’t really have lines you you you you can
Imagine it’s more like a flow like a flow of water or fluid so anyway so then we Define what it was called the flux okay the flux you can think of that as how many fied lines talking through an area and at the time we defined it as e do a
The area so we’re going to have the same thing we’re going to have to define a magnetic flux that’s going to be B dot a okay so it means you take a imaginary area okay and maybe you’re going to have some line magnetic field line maybe it’s
From a magnet poking through and you use that equation to find you know how many lines St looking for so it’s it’s like the the the example with the water and the little shrimps inside you know how many little shrimps you are going to catch so anyway my point is that if you
Take a magnet there is no monopole so it means you always have a north and a South so if you find a magnetic charge you will get a Nobel price and it’s always curling okay okay dble does don’t like to diverge doesn’t like to converge it’s curling like this okay so you
Have it’s it’s not very good drawing but you get the idea right and then as you move away of course those line are going to move away from each other that’s how it work so now let me ask you something now going in so this go in that out now
If I take like I did here for G slw if I take a imaginary so I take a imaginary surface closed surface here around the magnet so it’s like a bag you put your magnet inside what do you think is going to be the total number of lines
Poking for so remember in will be negative out will be POS exactly it’s going to be zero and the fact it’s zero it’s reflecting the fact that there is no monopole okay so we’re going to translate that using Vector calculus okay so math is just a nice way to
Express a concept that concept is here okay it means that the total flux of the magnetic field poing through a Clos area equals zero so this is called the G slw for magnetic for magnetism this is the integral form you can have here the differential form if
You take calculus that says it’s B cannot diverge cannot converge this operator here is a diver Divergent Divergent it’s a DOT this this is the D convergent okay so you see here that was G La for electric field if you take a bag around an electric charge yes it’s
Going to converge or diverge it’s going to be a source or a SN so the the the total amount of electric fing lines sping through the bag will depends on the charge inside the bag okay you see this are Maxell equations beautiful beautiful equations so it’s very good question
Very good question so for electricity electrostatic here electrostatic we had the Epsilon zero and that’s what we’re going to talk about for magnetism we’re going to introduce a new constant called mu0 okay so you have epsilon0 for electrostatic and you have mu0 for magnetism the beautiful thing about that
Is that Maxwell when he developed all those equations and he play with them by playing with mu0 and epsilon0 he got the speed of FL so he was able to predict electromagnetic waves just with the math and later on it was U the first electromagnetic waves were able to be
Were detected by Henry HS using a tank circuit right using a solenoid and a capacitor making the charge oscillate back and forth he was able to produce an electromagnetic wave like a microwave like the magnetron in in the microwave okay so this is called G slow for magnetism and there is no monopo
So the source of magnetism has to be moving charge okay so here I I took a in that slide I have all the equations that we’re going to see in this unit okay so it’s like a summary so first of all we’re going to define a new constant so
Epsilon0 was 8.85 * 10 -12 mu0 okay it’s called the permeability of free space it’s going to be 4 Pi * 10 to the7 so it has a long you know units here it’s very big uh if if you do four time 5 times this you’re going to get that okay one
One alternative unit is called the Henry Henry okay um per meter of this okay so you have a new constant so here are some equations you’re going to use if you you have a straight wire okay you can show using math that the magnetic field at a
Distance R will be this equation here okay so it depends on the current obviously but also on the distance so it’s inversely proportional to the distance okay it’s not inversely proportional to R squar because there there is no monopole now if you have a loop of current we’re going to see that the
Magnetic field at the center will be given by this equation here R is the radius okay so I will show you how they they Define so it’s a lot of heavy calculus so I’m not going to derive anything so and then for a solenoid okay
So if you have a solenoid so so solenoid has to be this but you need to have a lot a lot a lot a lot a lot a lot a lot a lot of terms so everything is very very very packed that’s how you can make an electromagnet in that case the magnetic
Field inside okay it will behave like a magnet a bar magnet like a bar magnet the magnetic field inside will be uniform and that will be the equation you have the constant this is called the density of loop so that means the number of loop per unit length and it’s
Dependent on the current so this is very cool because that’s how we make electro magnet of MRI and you see to control the magnetic field which is about constant inside you just need to control the current is that CLE so twice the current twice the magnetic field so very convenient we already did
That here you take your right hand again if you do this that will be yourself that will be the north okay so we talk about that so again as uh you you ask the question see here in the slide that will be the constant that we use for magnetism that
Will be the constant that we use for electrostatic and Maxwell who was super smart he did did something he play with those constant here and turns out that if you if you do one over the square root here you get the speed of light isn’t that amazing so all of a sudden
You do not have electrostatics and magnetism you have electromagnetism so he was able to predict the speed of light and later on it was U there was an experiment to find it okay so I’m not going to go into the details with the calculus because it’s quite heavy you have two French people
Here one is called biot Jean batist since he’s French I’m going to say his first name Jean batist b b okay in French and the other one his name is Sav or Felix sa based on experiment so the goal here is to find a a useful equation like a a formula to be
Able to find the magnetic field anywhere in space because of distribution of current right so you have some kind of distribution maybe it’s a loop maybe it’s a solenoid maybe it’s just a square like a current going through a square or a stretch wire so you need to find a way
To find that magnetic field so this is given by this equation here it just say that if you have a small current segment okay at that point in space it’s going to make a small magnetic field here so you have it’s a cross product so you have to use your right hand magnetic
Field will be in that case into the Bol and it will be given by this equation here but you see it’s D okay it’s a small b a little bit of B so if you want to find at that plant the real magnetic field you have to
Ingrate very good over the all wi so it’s it’s heavy with Calculus and but you can use coding okay so here you have a link to a free book and it’s going to show you how to do the integration so if you are into calculus you’re going into engineering I
High Rec command to to look it up how it’s done so anyway if you integrate you are able to find the magnetic field produced by a straight wire okay so you say your thumb here would be the stretch wire and L is not here no stretch wire
And and it’s the magnetic field is going to curl around okay so it’s inversely proportional to the distance and not inversely proportional to distance Square because you had to integrate okay so that will be the equation you you if you want you can simplify you can simplify that equation
Here because you have b equals mu I over 2 pi r is that right okay so if you want to simplify you can say 4 Pi * 10^ -7 I over 2 pi r so that goes so b = 2 * 10^ the7 I over R so that will be the
Equation for the magnetic field of a stra trial if you want to memorize it or or or if not you just use this equation okay we already talk about that you see here it’s going to be very strong as you move away it’s going to be so uh the magnetic field like to
Circulate so this I highly recommend that you work on that I’m going to save it for something good idea if you try to do it so let’s Cho to to to do this one using that equation here using the equation that we just have seen you so what’s the
Idea you have a straight wire of course it’s going to be connected to some power supply so at that point in space it’s going to make a magnetic field you see you take that that spot here you make a radius so the magnetic field wants to circulate so it’s going to be
Perpendicular here to this here to that distance there so you have a magnetic field because of a straight wire and then comes a charge and the charge has a velocity V so it’s a two two steps problem first you’re going to find the magnetic field produced by your straight
Wire and then you have a charge a positive charge here moving in this direction that velocity is perpendicular to B so it’s going to be acted upon by a force again you take your right hand okay so do do that so you go in two steps you don’t
Stare uh yeah you do you do help each other talk to each other you’re finding the force yeah you’re finding the force so first you find the magnetic field by the way there is a career fair at BBC I think it’s BBC on April 4th a career fair you have to check
A handshake so what’s the equation mu0 I 2 pi the distance so we are looking at the magnetic field at that point remember you take your right hand up is your wire and the magnetic field wants to go around you see you have a magnetic field all around and here you have the
Magnetic field this way so first we’re going to find the magnetic field you can use the equation so 4 Pi * 10^ the -7 and then you have the current which is three and then you have 2 pi * 0.05 you can simplify so so b = 2 * 3 6 and 10^
-7 over 0.0 five are you doing it I forgot my what what you get yeah 12 micro okay and then we want to find so here you have the magnetic field all around it’s circling around so that’s that SP here by the way it’s going be the same
Magnetic field all around now you have a moving charge okay so that magnetic field is going to act exert the force F will be equals to q v perpendicular to B times P okay so the magnetic force will be Q so 6.5 * 10 the 6 the speed is
28 and then you have 1.2 * 10^ the5 22 22 okay n Newton or 2.2 * 10^ the 7 Newt okay so that will be the magnetic force eight or Seven is that eight I have Seven oh there is no answer so make sure you is that 2.2 * 10 to8 okay so you’re right mistake let’s go back to my not okay so this one it’s a big challenging but um so you have you have uh currents going into the screen so you
Have one wire here one wire here one wire there and it’s a current flowing in those wires and they go into the screen okay so remember you have to be able to do that with your hand okay or you can imagine so if you have a wire like this
Like this in the screen the magnetic F will go around like that can you do this into the screen it’s going to describe you know uh we used to have what is called a compass so something here and you go around like that and it’s going to make a circle
Right in school we used to have that I don’t know if I still use it oh to make a circle so you have a magnetic field going around a circle around two around three one you need to find a magnetic field at P magnetic field is a vector so
You need to find the net Vector so you need to add all those individual vectors so you have magnetic field by one you have B1 and then B3 and then B2 you need to add them up as a vector as vectors so it means you need to find the X
Component the Y component and then you can find the magnitude okay and um so the first thing you want to draw let’s draw first let’s draw the magnetic field from I3 the magnetic field from I2 and the magnetic field from i1 and again in your head you have
To take a what it’s called a compass that’s going to be the current and then the magnetic field goes around like this right you have to do this okay so first we’re going to make a drawing so no staring you cannot stare so first we want to draw the magnetic field from I3
From i1 and I2 and again you do this into the screen with the thumb and you go over and my back out okay so don’t do it do it do it and then we do it’s a nice review of vectors but I don’t want to stay too long on it
Okay let’s do the drawing first so this one is easy do you see that um the magnetic field is going to circle around do you see it right so at that point where is the magnetic field you go like this imagine imagine you have a string
Here and you go all around here so the magnetic field will be at that point it’s going to be up down left or right very good what’s your again L yes down so it’s going to be I one is going to make B1 do you agree so this one also is easy imagine
You take your thumb you shove it into I3 and you go around like this right so it’s going to make you go around let’s see you go around I’m going to take green you go around around I3 I supposed to make a circle here so where is B3 this way do you
Agree so that will be B3 and the way you see it is that you see the B is always perpendicular to that distance here between the source and P okay cuz if you have a source here and you have a point there that will be your current I that
Will be the radius of the distance you see B is always perpendicular to that okay it’s perpendicular so it’s going to be perpendicular and let’s find from B2 try to do it so that will be my distance here it’s supposed to be a square it’s not it doesn’t look like a
Square it’s supposed to be a square and again it’s going to make a big big big big big big big big big circle okay so it’s going to be perpendicular here so that’s going to be B2 so you have B2 B3 and B1 and it’s a square because it’s a square
So that that that here is going to be 45° it’s it’s supposed to be a square not a rectangle it’s to be a 1 cm 1 cm okay so if you have something here so that would be B2 that’s going to be 45 degrees okay so little bit of geometry and
Um don’t space out so it’s the magnetic field at Point p and now these are vectors so I need to find the X component the Y component and then add them up okay they’re not pointing at P so you make a circle around that’s going to be the magnetic field here from
I2 this from i1 you make a Circle that will be B1 and from I3 I3 is going to be here okay at least with the course for the no they want to find the net force the net magnetic field yeah but we’re going to find out because we’re going to use algebraic method
We’re going to find the X component and the Y component so how do we figure out you need the um you add vectors you can do the the type to head so in that case B1 will be equals to B2 right so when you add them up you’re
Going to get the diagonal and the diagonal will add up to this one so that will be a way to go faster actually okay this B3 and B one are the same in magnitude so when you’re going to add them okay it’s going to be the parallelogram
Method so it’s going to be along the diagonal and then you add B2 right I’m I’m going to do the long way I’m going to do the X component and the Y component okay so when you have vectors to add the first thing you do is just find the magnitude okay let’s forget
About X component y components because X component will be with cosine and Y let’s find the the magnitude so B it’s a square okay so this is 1 cm this is 1 cm so that distance here is going to be the square root of two which will be 141
CM okay it’s it’s supposed to be a square I don’t know why it doesn’t show a square so B1 just the magnitude so it’s going to be what what’s the equation it’s going to Be 4 or 400 so did you do mu Z 2 * 2 two is that a two pi oh yes you right you have the current here and the distance 0.01 so what so I found okay micro so four * 10 to the negative um five okay so we agree
Do you all get that right you you stck here so do it with me guys so will be the same as B3 okay because they are the same distance B1 and B3 will be the same and then we need to find B2 so the distance for B2 it’s going to
Be the square root of two don’t space out I see people spacing out don’t space out do it do it more you do here L you have to do at home so it’s going to be mu0 two and then you have 2 pi 0.141 because that will be square root of
Two and you get about huh what you get guys do it do it do it do it again 2. 83 * 10 to the5 Tesla do you agree that that will be the distance here if it’s a square you use Pythagorean theorem 1 square + 1
Squ equals that distance okay so a sare + b² = c² so that will be a square root of two okay so you have to convert to meters okay so then we can Define the XY Co system so B3 has a x component it’s an X component
B2 has X component not B1 so you’re going to do X component equals minus B3 right so – 4 * 10^ the3 and then the X component for B2 you need to have the cosine cine 45 so that would be for the X component do you understand remember
From physics one how to add vectors using algebra you need to add the X components you need to add the Y component and then you take the magnitude okay don’t stare do it do it do it do it do it and you get get min – 6 no there is a five
Here it’s a five here why did I put a three so – 6 * 10 the -5 test for the Y component you see because it’s everything is symmetric you’re going to get the same thing okay so you have a x component here for the net magnetic field you have
A y component they are equal to each other so now you can find the net magnetic field here and you use Pythagorean theorem okay so B will be equals to what you get okay we we have only like 10 minutes so can you do it don’t don’t space I I
See I feel I feel that some of you are spacing out don’t space out that will be the magnitude okay now if you want to put the direction uh how do we put the direction that will be in this direction here so that will be the magnitude at 45 degrees 45
From from the negative X AIS or from oh okay you can figure out the angle doesn’t matter so that’s going to be the magnitude okay it was it’s not easy the idea is that you take your form you imagine you have a your hand becomes a compass and you go
Around like this right like this positive no there is no charge here is the current oh here there is no charge I didn’t place any charge yet so if I if I do place a charge then it depends where is it going you will have to find the velocity uh perpendicular to
B so velocity here so it will Circle or around the magnetic field so if you put a charge here it has to be moving yeah yes like this and and I didn’t put a charge they just want you to find the magnetic field at that point and if I put a charge if
It’s moving and if you have a component perpendicular to B then it will be acted upon by a charge okay you’re not sping out okay so you see here I don’t know if it’s in my canvas by the way on canvas I put the movie for the video for magnetron it’s
Interesting uh so you have a free book here this is free okay so then here is another equations if you have two wires okay parallel to each other for example so in that case they are parallel to each other you can see that one wire okay it’s going to make that
Magnetic field curling around so at that point at that point you can take your right hand so the current is going this way magnetic field is going up where is the force to the other wire of the way are you sure so let’s see the the current is going this way
The magnetic field is up so you want to find at that point that point here the intersection here that point the magnetic field is up see here the magnetic field is up here is in this direction so the magnetic field is always tangent to the magnetic field
Lines like when you have an electric field lines the electric field is always tangent Two current two parallel wire and they flow in the same direction so the current flow in the direction they going to attract each other if they flow in opposite direction they’re going to repair each other okay you can show that here so if you are the same political
View you love each other opposite politic View and you hi each other just wa to remember discuss the equation for solenoid and not yet it comes at the end so it’s attracting do you understand so that’s why the wires the wires it could be annoying they they have a force
Between them so if you have Transformers so you know those ugly Transformers next to the bridge to Sunny eyes you have a big station with all kind of Transformer very ugly it’s ugly because in here you can have you cannot have anything in the ground obviously because we on water so
Everything is above the ground so it’s very ugly but anyway you can hear the H it’s always making noise that’s because inside the Transformer you have wires okay and you have AC so the current flow in One Direction the opposite direction so the the the wire always acting on each other
So they always vibrate it goes like this right so let’s see if I have a video very quickly it’s it’s a super cool um if I find because force on the current caring wire is that this one so I have here a large magnet No is that attraction Force still present ins yes the magnet it’s a good question magnetic field doesn’t care about insulator electric field yes not magnetic field so parad cage work for an electric field not for a magnetic field you cannot escape a magnetic field so you have constantly magnetic field going for
You all the time right so it’s going to induce a currence inside you I don’t know if it’s very hey not sure I I just need to find um there is but it’s just that I don’t find it maybe here somewhere no here so they have a power supply which
Is a 12vt battery and then they have a wire so if if the wire is in series okay you have one wire here and the other wire there and you do this okay you do that can you see that I’m going to break something so you see here if the current
Is flowing in this direction that direction so they will be opposite right so one electric one current flow in this direction the other one will be flowing in that direction so it will be in opposite right but if they are in parallel so I have a circuit in parallel
With two wire they will flow in the same direction that’s how they did the experiment so did you see how they repell each other so do they flow in the same direction or opposite opposite very good right they hate each other so it’s very cool so imagine you have a
AC so it will be constantly vibrating and that’s why that’s why it makes some noise it’s a it’s a very nice setup so if you go to YouTube they have a channel MIT demo and they have great demo so of course you need an equation
For that okay you can you can do the it’s it’s not hard to show so you you find the magnetic field here produced by this one and then here you have a flowing current and you have the equation for the force on the on the current carrying wire so you can find the
Force and you you end up with this equation so that will be the force per unit L and you see that it’s proportional to the current in one proportional to the current into and the distance between them you don’t need to do the math it’s it’s it’s your guts
Your gut can talk to you it makes sense that the force depends on the current in one the current in two and it’s going to be inversely proportional to the distance okay because the B is inversely proportional to the distance assing that I is the
Same which one do you see I square or the second equation this one so it’s I2 yes so the the I2 the the current the current flowing here okay so let’s um we we we’ll do the math next time but you have a loop of
Current do you think it’s going to be at the end so I’m looking at the Loop is the loop going to be attracted or repair because this one is going opposite and this one is going to be um in the same direction so so we repel because the distance here is
Smaller okay so that force will be stronger that Force here will be attracting but no this force will be larger and this force will be stronger no what did I say the force here will be stronger because the distance is smaller and that force will be smaller because
The distance is larger so it’s going to be repel here and this one will be attracted so we repel wings and you can do the math again you have two forces and you have to add them up because these are vectors and and you see it comes from
Here which is another free book there are so many free book I I lost uh see it’s a free book