hi everyone welcome back to everything is relative with me Mr K today we'll be doing a crash course on the topic of magnetic fields for Cambridge a-level physics 9702 now remember our crash courses are just meant to cover at a very high level the concepts and the topics the subtopics that will be important to understand for the exam so it's not going in depth but simply covering everything at a very high level now magnetic field is one of the longer topics if not the longest topics in a levels in Cambridge a levels at least so for caie there's a lot to know and a lot to understand and it can get overwhelming but that being said if it is the longest topic with the most amount of Concepts it is highly possible that that could be a fair portion of your examination so it it's no good to to leave out or omit the section when studying so we'll try to break it down as simply as possible it's a lot of stuff to cover so we're going to move at a fast pace as well but this again is just to bring you back up to speed with everything that you may have forgotten during the term now what do we know about magnets now without going into the detail of why this happens you're most more than likely would have seen a magnet at some point if it's in the school lab you'll see one that's that looks similar to the bar magnets that I have here they have color-coded and they have a North and South Pole they always exist in two poles and if I bring a north and a South Pole close to the to each other we know there's an attractive Force so these are called bar magnets to be specific because they are in the shape of a bar and we have unlike poles near each other and so what we realize is that unlike poles attract and if I bring two North Poles to each other near to each other or two South poles for that matter any like poles and the opposite will happen there's a force between them but now it's a repulsive Force so we say like poles repel remember this is not analogous to the force between charges because that exists as a monopole a charge can either be positive or negative but a magnet must exist as a South and a North Pole there doesn't exist magnets of jest of a North or a South Pole so what we first need to discuss is the topic of field lines more specifically magnetic field lines now you would remember from gravitational fields that we had gravitational field lines and these basically tell us the same thing or a similar thing in essence these are lines of magnetic force so if we follow the lines of a magnetic field we follow the lines of the force and in this case magnetic field lines tell us the direction of a free North Pole direction that the free North Pole would move if it were placed in a magnetic field so let's just copy and paste our magnet again just make it a little larger now there are forces that will be exerted in on another magnet if it were to come close to this magnet but we need to visualize these forces so the field lines are imaginary they for us but it gives us an idea of how the field can be drawn so I just rotate it so that my knot pole is in the left doesn't really matter and if I were to draw field lines I notice that the field lines start on the north North Pole and terminate on the South Pole and so even for just a single magnet I have a start of a field line and the end of a field line again excuse my drawing but as we go further from the magnet then the field lines are not as tightly packed onto the magnet and you can see we start in the North End on the south of the very same magnet and if you did this experiment with iron filings you would have seen this pattern emerging obviously without the arrows but you would have seen a very similar pattern emerging with iron filings if you place this magnet under a piece of paper plain white piece of paper and you scatter the iron filings over the piece of paper and you notice that these patterns emerge that's because the ion filings which are magnetized themselves will follow the lines of force follow the magnetic field lines and so we get these field lines kind of a nice symmetric pattern to them and so this is for a single bar magnet so a field line starts in the North End on the south and so what happens if I bring opposing poles of the poles of opposite of two different magnets together so let's first do this for again we can make these quite large just so that it's easier to observe so if I bring a North Pole of one magnet close to the South Pole of another magnet what happens is the field lines do exactly the same thing they point from north to south and unless the surfaces are completely parallel or completely completely parallel to each other then the field lines will curve and Arc out of it okay so they're not all straight lines so the feel is not always uniform it's not uniform between two magnets and so again you would see a very similar pattern if you now replace a single bar magnet under your piece of paper with two Bob magnets starts on the Note ends on the south that you wouldn't be able to observe but the pattern the shape of the lines will look very much the same and then if I if I now bring leg poles together notice how the the field lines all join the two magnets they go from one Magnum to the next so if I were to throw in if I could for example find a free North Pole if that could exist and I drop the North Pole here the North Pole will be repelled from the North Pole of the first magnet and attracted to the south of the second and it'll follow the path along the field lines if there was a free if there was such a thing as a free North Pole now if I change the scenario just just slightly if I simply take the magnets and now bring the North Poles next to each other and the field lines look very different again this can be easily achieved with the iron filings so now they exit from North Poles and they are repelled by the opposing North Pole and so basically what happens is that they move away from each other they leave a nice big empty space in the region between the magnets the space in the center is a space where there's little to no Force where is it a pulsion and these two magnets will repel each other but there is a neutral point somewhere somewhere in between so if I placed a free North Pole right at the center it would experience no Force the forcer the force in the right hand magnet will balance the repulsive force from the left hand magnet and it will just remain stationary and so it's clearly different when we have leg poles and unlike poles near each other some of the rules of field lines again this will be in your textbook you need to read and understand but the reason why we use field lines is simply so we can have an idea of a visualization of what the force would look like if I throw a North Pole in there where would it move similar to the field lines for electric charges if I throw a positive charge in the field lines where with a positive charge move and so what we know about felines is that they start at the North Pole I'm going to write this in shorthand obviously for you in a question you'd have to write this in a full sentence or as a full sentence start at the North Pole terminated the South Pole we also know the field lines never cross why do felines never cross because that would be ambiguous we cannot have two points anyway in space would have two forces coming from the same object okay there should be one force and only one force and so if the sphere lines cross that would be that would be ambiguous that wouldn't be uh it's non-physical um they also I'm going to write this in short form give the direction like I said of a free North Pole or an isolated North Pole that's the direction a free North Pole would move if it was thrown into the field if there was such a thing as just a free North Pole which there isn't and the last thing that field lands do is indicate the strength of the field how strong the field is so I didn't make this very clear in the diagram but the field strength is indicated by the closeness of the lines so what you would notice is as we get further from the magnet the field lines are consecutive field lines are further apart and what this means is that the field is weaker further from the magnet which sort of makes sense as you get further from the magnet the magnetic field strength is weaker if you pull these magnets very far apart you'll notice the iron filings don't have much of a of a defy well-defined shape anymore and so that's why the distance between consecutive field lines will tell us the strength of the field so as you get further from the magnets the field gets weaker the magnetic field gets weaker so closer field lines means a stronger a stronger field and so if I wanted to define a magnetic field it's not that easy to define a magnetic field but we'll try now we have to be very careful that we don't confuse a magnetic field in an electric field and something very important that distinguishes a magnetic field from an electric field now a magnetic field is a region of space like any field is a region of space where something feels a force now that something is very important because this will make or break the definition where a moving charge moving charged particle or permanent magnetic Pole experiences a force why can't I say just charge why can't I simply say charged particle okay why can't why do I have to say moving charge well that's purely because by saying a charge particle we could also be including stationary charge particles if a stationary charge particle is feeling a force it's not necessarily feeling a magnetic force it could be feeling the electric force so only moving charged particles like we'll see later on only moving charged particles feel a magnetic force stationary charged particles will not feel the magnetic force so we will see that later on but magnetic poles will always feel a a force in a magnetic field okay so a permanent magnet will always feel a force in a magnetic field so the first thing we want to discuss about some of the usefulness or the uses of the magnetic field is the motor effect it's called the motor effect because well it's the effect that allows Motors to operate what is the motor effect well simply will bring back our our magnets so let's say I have the North Pole of one magnet facing the salt pole of another magnet now since the notes The North Face and the South face are parallel to each other at least at very close distances we notice that the field lines will be uniform we have a uniform field in the region between the faces of bar magnets now if I place a wire in that field so this is a copper wire and if I place this wire in the field what I notice is that nothing happens well that's great all this drawing for nothing to happen feel still continues to go but there's no current in this wire it's just a neutral wire and nothing happens to the wire but I'm going to change the scenario very slightly I'm going to leave the magnets as they are okay not to South and so the field lines point from north to south I'm going to redraw this diagram with one small change and that is that current is now flowing in this wire so now I have a current in the wire and we notice something strange beginning to happen the wire feel the force this is in very simple terms the motor effect there is a force on The Wire so when current flows specifically when current flows at some angle to magnetic field lines then the wire in which the current is Flowing feel the force what we sometimes say the current is feeling the force and so that's quite an important concept to understand that when only when the current flows will a wire feel a force if I remove the current then there isn't a force now remember this force will make the wire move either to the left or to the right it will be repulsive or attractive or move in or out of the page something it's a force so what's important about a force always is two things since it's a vector we need its direction and we need its magnitude and normally we usually go straight to the magnitude first and then figure out the direction later since we aren't studying vectors in this course we're going to have to use a trick well I wouldn't call it a check we have to use a little piece of imagination to find to find the direction of this force and we use something called Fleming's left hand rule which looks something like this so if I take my left hand and I curl my fingers in such a way if I extend my fingers outward in such a way that my thumb my index finger so my thumb my index finger and my middle finger are all at right angles to each other so you notice F and B are at right angles F and I had right angles and I and B are at right angle so I essentially create a right-handed system where all three fingers are 90 degrees to each other what I have is an idea of how to use Fleming's left hand rule so if I can position my hand in such a way so as to match the diagram that I'm looking at in which I want to find the force the magnetic field or the current then I use the left hand rule the thumb gives the direction of the force so F here is the magnetic force that is felt by the wire as the current is moving B we haven't defined B just yet but just think of B you've already studied this topic so you know that we use the symbol B for the magnetic field remember the magnetic field is pointing in a straight line we're only considering considering uniform fields a uniform field always points in the same line and so it's pointing in a straight line along the index finger and the middle finger gives us the direction of the current so I have to match the direction of the current with what I have in the diagram if I were to think about if I were to copy right we look at this diagram and take this diagram and I'm going to bring it up here next to the the magnet at the bottom so what I'm going to try to do actually I can't do it with this diagram but what I would do is I would take my middle finger and point it upward just be wary if the surroundings when doing so I will notice that my field is pointing from left to right B is pointing from north to south left to right so in that scenario I have B pointing from left to right my middle finger pointing upward and so my thumb naturally will Point into the page and so what does this mean this means that the force on The Wire force on The Wire is into the page remember these three are all perpendicular to each other so something's going to be going in or coming out of the page it turns out in this case the wire will be pushed into the page if I reverse the current and I use the left hand rule again then the current the force on the Y will be out of the page okay so that's how we use Fleming's left hand rule and so if I were to draw this as a three-dimensional or right handed system then what I'd have is that my Force field and current are all at 90 degrees to each other and so yes you could use Vector methods to work this out but that would be a lot more complicated unless you are very very confident that you can do the necessary Vector calculation so we use the left hand rule to avoid using unnecessary vectors now that we have the direction of the force we need to find the magnitude of the force the size of the force so the size of the force also can be fairly difficult if you're not using calculus and vectors but if I had a wire carrying a current I at some angle to the felines now we're not going to assume that the current and the field at right angles okay so it's possible that the current and the field are not at right angles it could be that the current is at some angle to the field then the left hand rule become a little bit more difficult to use so if I have the field B again we give magnetic field strength or magnetic flux density to give it its real name its true name symbol B the angle between the two is Theta and the length of this wire at least the length of the wire in the field is L the amount of wire in the field we call L now what we have is that the force on this wire is proportional to i l sine Theta okay but what we actually want is the perpendicular component of the force which is actually we can convert this let's first convert this into an equation we get f is equal to remember going from an if you're going from something that's a proportionality to an equation we have to add a constant of proportionality in this case the constant is B so f is b i l sine Theta where B here is the magnetic flux density we'll come across the word flux a little later on but the actual name for B is magnetic flux density and if I rearrange the equation above I can get b is equal to F divided by i l sine Theta now why do we use sine Theta it's simply the component of the force that is perpendicular to the current or the component of field that is perpendicular to the current it gives us the maximum amount of force if the current at any point becomes parallel to the field the force becomes zero because Theta becomes zero for Theta 0 or 180 degrees sine Theta is zero there's no Force so the current the wire must be at some angle to the field lines in order to feel a force if I want the force to be a maximum sine Theta must be 1 which means Theta must be 90 degrees and so when Theta is 90 degrees when the current and field are perpendicular then the force simply becomes f is equal to b i l so the sine beta will disappear if Theta is 90 degrees okay so if we have this expression for B this is where the definition for magnetic flux density comes from if they ask you to Define magnetic flux densities what are the more difficult definitions simply look at this equation B is f over i l sine Theta it is the force per unit current per unit length oh but the sine Theta is a bit annoying so let's write it as F over IL if Theta is equal to 90 degrees okay this makes it a bit easier to do the definition so the magnetic flux density B is the force per unit current per unit length on a current carrying conductor that is perpendicular to the magnetic field ah okay so it is a force per unit current per unit length on a current carrying wire on a straight current carrying wire placed perpendicular to the field there we go the definition array arises from this equation and so if Theta is equal to 90 degrees F is simply both f is bow when Theta is 90 degrees and B is equal to four at F divided by Il and so from here we can see that the unit of flux density is Newton per meter per ampere okay but we give this another unit to make sure that our laziness is intact and we call this unit the Tesla uppercase t for Tesla named after Nicola Nicola Tesla and so the unit of measurement for magnetic flux density is the Tesla okay now that we have the mathematics out of the way we can talk about the force on a moving charge now why did we suddenly go from a wire to a moving charge well it's simple it's not purely the case that the wire is feeling the force due to its inherent properties it's the fact that a current is made up of moving charges that the Y I feel the force and so if an I if I isolate a single charge a single charge Q any charge particle an iron an electron a proton whatever it may be and I place this at some angle to a magnetic field think of what I'm what I was doing earlier but now instead of an entire wire of current I only have a single charge it's moving with a speed V which in many cases will be the drift velocity of any wire again let's not assume that let's assume it's moving freely in a magnetic field which will Define a magnetic field that has a flux density of B and Theta is the angle between B and V and what happens is the force on this charge particle and we aren't going to derive it but it should be in your textbook and you should know how f is b q v sine Theta and this gives us the magnitude of the of the force that a Charged particle feels when it moves through a magnetic field now this is why in the definition of magnetic field I said that it has to be a moving particle because if the force depends on the velocity if it's not moving if this charge was stationary guess what the force is zero as well there's no magnetic force on a stationary particle on a stationary charge particle and if I wanted to find the direction I have to use Fleming's left hand rule now I want to make it very clear that as I didn't point this out earlier Fleming's left hand rule gives the direction of current when I say current I mean conventional current I mean the flow of positive charge so if this were if this were the case of electrons you would flip the direction of your middle finger okay conventional current is the flow of positive charge if you were electrons flowing you would flip your hand so that your middle finger points in the opposite direction a conventional current flows in the opposite direction to negative charge okay so that is how we find the force on a moving charge now it turns out that also something very I won't say peculiar but something a little bit odd happens when we move a charge into the region of a magnetic field so looking at this picture we have a very weird diagram what this means if you see a circle with a DOT like that is that the field is out of the page if the field were into the page we'd use a circle with an X we look at another example that has something like that later on but a circle with the dot in the center means the field is pointing into the page since I can't use an arrow because of the using a two-dimensional plane I can't see the arrow and so I use a DOT to say that it's going into the page then I have a charge on its merry way as a charge q and a mass m and moves into the magnetic field now I use Fleming's left hand rule it's a positive charge moves into the field which is pointing out of the page and what happens is it'll feel the force but it turns out that the force it feels is always at right angles it's always at right angles to the charge and so what happens is at every point there is a centripetal force acting on the charge particle and because of this it moves along the Arc of a circle and it continues to move in a circular Arc as long as it is in the field if you notice this diagram if the field were large enough it would just move in a circle That's the basis behind the principle of your magnetron your cyclotron inside your microwave oven for example we can spin charges in a circle if we have a magnetic field large enough but if it were to go in and then leave it enters by moving in a straight line there's no other forces acting on it the force acts at right angles the magnetic force acts at right angles throughout its time inside the field and then when it leaves the field again it continues to move in a straight line but as long as it stays in the field the force on it the magnetic force on it is b q v Theta is 90 degrees because the Velocity in the field are always at 90 degrees to each other since the field is pointing out of the page and the velocities along the plane of the page but this from our knowledge of circular motion is MV squared over r where R is the so if this was a circle there'd be a radius on the center of the circle to the center to the point on the circle and that radius is r and so that's equal to MV squared over r that means the radius of the circular path if I do a little bit of mathematics here is MV over the flux density B times the charge Q now what I know is that the Master charge ratio M over Q is actually constant for all charged particles and it's Unique for all charge particles every single charged particle whether it be it's an ion or a proton or electron has a unique value of M over Q that's very important because I can use the size of a radius of the Arc of a Charged particle to find its velocity or to even find the field strength B so this is a pretty neat method of determining if I also can determine what the velocity and the flux density are if I know what the Velocity in the flux density are I can find out M over Q using this expression and so I can identify what type of particle what type of charge particle is going into a magnetic field very interesting application it's used in Spec spectroscopy to determine what type of particle we are looking at what type of gas we are looking at if we ionize the gas and get it to move in a circular Arc inside a magnetic field the radius of its circular motion tells us exactly what particle we're looking at okay the next thing whether we're moving at a quick Pace but there's a lot to cover is velocity selection now like the name suggests it simply means we need to select a velocity so we won't talk about the applications too much but imagine that we have a scenario where I'm going across Fields now I'm going to have an electric field you remember your topics of electric fields and capacitance a uniform electric field points from positive to negative and so the electric field points downward and we also have a magnetic field with looks which looks as follows so let's assume we have our electric field pointing down with our magnetic field and now we get to use the crosses so the circles with crosses means that the magnetic field points into the plane of the paper into the page and I have positively charged particles moving into this region of the field now if positively charged particles move into the field then what I know is that the electric field will pull these particles downward what I also know is that the magnetic field will do the opposite the magnetic field will pull these charged particles upward since the magnetic force will be upward if we use slimming left hand Fleming's left hand rule and so if I want particles to move straight through undeflected and let's assume I put something to capture these extra charge particles if I want these charged particles to move straight through and be undeflected remember I have a force FB pulling it up and I also have Force f e pulling particles down so now it turns out that it turns out that if I want the particles to move undefect deflected then the forces must balance the upward Force must balance the downward Force so f e must balance FB and this is Q times E from our topic of electric Fields this is equal to q v b b The Q's cancel I'm left with v equal to E over B so any particles that enter with a speed of e over B will exit without being deflected V is equal to E over B if V is greater than e over B what does this mean it simply means q v b must be greater than QE charge is the same okay so they will be deflected upward the magnetic field is stronger the faster particles move the electric force doesn't really care about its speed and so if the speed is really slow the electric force takes over and pulls the charge particles downward so V is less than e over B and this comes from the fact that q v b is less than QE so I can select particles let's say I only wanted particles of a certain speed I can apply this velocity selection to absorb particles to remove particles that don't have a speed of e over B why because if I set the values for e and B I can choose exactly the speed V of particles that I want maybe I have an experiment that purely wants a certain that needs a certain speed of particles and I can restrict the speed of particles by doing this okay so I keep this Gap small enough so that only particles with the speed V is equal to e over B can pass straight through okay so if I were to draw the charge free body diagram force diagram the left hand rule tells us that the magnetic force is up and a knowledge of electric Fields tell us that the electric forces bound and so we can balance these two forces so that the particle continues to move from left to right okay so that's a little bit different that's the topic of velocity selection it's not too difficult but the next one is a little bit more tricky okay and this is the topic of the hall effect now I know many of you want to omit this from your studying leave this out I wouldn't suggest this because when you take the time to understand it you realize that it's not that bad okay so let's draw a diagram to see what this looks like so I'm going to consider some conducting material I'm going to take a slab of some conducting material it doesn't really matter what kind of conducting material this is so this is a slab of a conductor and to draw a small cross section of it like I have done here I'm going to apply a magnetic field downward I'm going to use something that will generate a magnetic field downward onto this slab of material and so I'm going to call this magnetic field I'm going to give this magnetic field a flux density B and at the same time so let's also label parts of this conductor this conductor has a thickness T lowercase t and what I'm going to do is I'm going to pass a current through this conductor perpendicular to the face at the bottom perpendicular to face let's call it a b c d okay again this is a common past exam question in the absence of a magnetic field what would happen is the current would pass straight through the conductor it would be on deflected it will pass straight through the conductor and so let's just give this current a name as well we'll call the current I as we usually do now what happens in this case is we have a magnetic field now again this is and we're also going to assume that this is electrons because we said Fleming's left hand rule works for conventional current but this is a physical situation it's a physical thing that we can observe and so we'll stick to the physical idea which is electrons flow and they flow through this conducting material nice and freely and what happens is that these electrons flow and deflected it there's no magnetic field but using Fleming's left hand rule you have to be careful about the direction of your middle finger the middle finger does not Point into a b c d but now points out of a b c d simply because it's negative these are negative particles moving in your index finger points downward because that's the direction of the magnetic field and your thumb which is the force points to the right and so the force acts on the electrons to the right so what happens is these electrons curve off and begin to pile up on the left hand face and so what we get is electrons on the left hand face so the left hand phase we can call it b d uh we give it random names p d l m electrons gather on the face be our d m aha so that makes the face negatively charged because I have electrons all piling themselves up on the left hand face and then positive charge as a result of the overwhelming number of legit negative charges lining themselves up on the right hand face positive charge is induced on the opposite face we won't have to give the opposite face a name but the face opposite the side opposite the negative charge obviously becomes positively charged and so what do we remember if we remember from the topic of capacitance if I have two lines of charge one positive and one negative I generate a potential difference and an electric field e so there's a potential difference V between the two faces and so what we call this is we call it VH so it's named after the person who discovered it Hall and so we call it a whole voltage it is simply a potential difference that exists between the faces oh okay so what does this mean now electrons can't move to the negative phase anymore there's an overwhelming amount of negative charge it repels them they move with the field lines against the field lines rather since they are negatively charged and they begin to move towards the positive phase so they feel it a force that will pull them to the left so they were initially moving to the right but they will feel a force starts to pull them more to the left but we aren't going to go that far it's gonna decrease the amount by which they are deflected until eventually they just move along the blue line so what we have is that the electrons will be pulled toward the positive phase which is the opposite phase and at some point the electric field the electric force will equal the magnetic force the electric force pulling to the left balances the magnetic force pulling the electrons to the right and guess what the electrons are on deflected now you're probably thinking why go through all this trouble to just let the electrons flow straight through anyway and the reason why is because and again I'm not going to derive this but it's a very important equation VH is actually if I connected a voltmeter across the two faces and I measured the value for the potential difference I get VH the whole voltage the whole voltage tells me that VH is B times I the flux density times the current over little n which is the number density of charge carriers that depends on the material that you're using times the thickness of the material times the charge which is in this case is the charge of an electron this is called the whole voltage so the whole voltage is set up once the force the electric force is equal to the magnetic force now the reason why we go to all this trouble is so if you look at this equation if I connect a voltmeter and I find VH if I know the current I the number density of charge carriers I know if I know the material for every material that's unknown the thickness is also known and the charge of the electron is also known what that means is I can use that to find the flux density it is the most used method of finding the magnetic field for an unknown field if I want to find the strength of a field I use a hall probe a whole probe uses a thin slice of metal rather a thin slice of semiconductor to find the whole voltage or rather use the whole voltage to determine the flux density so all probes have a known value for i n t q and with the value of VH that is found when you place a whole probe into a magnetic field B is then determined that's why we go through all of this trouble to find the whole voltage so you see it's not that difficult it does require reading but if you read it a few times if you maybe pause this video rewind it slow it down it's not that bad and especially if the question gives you the diagram and says hey tell us which face the electrons move to uh tell us which phase the positive charge is located on Etc it's not impossible to understand now the next thing we have to talk about is the magnetic field of a current now we spoke about what happens to the force on a current what about where does this Force come from why does it exist and that's because a current carrying wire I'm just going to draw it as a straight line so this is a straight current okay it's a current moving in a straight line so I'm simply going to call it a straight current so what we notice is that this is vertically upward and again my poor drawing skills are being showcased here what I get is that the magnetic field is a loop pattern it's circular so for a straight current I get a looped or circular magnetic field pattern and the other way is also again just picture this in your mind as a loop of wire okay now it doesn't look like that but this is a loop of wire so this Loop of wire means that current flows in a circular path the current flows in a loop well guess what to maintain the Symmetry we call this a solenoid or a solenoid what happens is that as the current flows and we can assume the current is flowing in any direction we have the field lines a magnetic field being generated by the current and this field is uniform inside the loop so inside a loop of wire the field lines are uniform and so we'll just write this as instead of straight field lines we'll write uniform magnetic field so anyway inside the loop the flux density is constant and the flux density direction does not change it's always left to right in this case so that's interesting thing and that's why wires feel a false when placed near magnetic field because they also produce their own magnetic field and only the two Fields can interact and that's why there's a force of attraction or repulsion and so a straight current produces a loop magnetic field a looped current produces a straight or uniform magnetic field okay if I had a flat coil it's one of those in your textbook so if I were to draw simply one Loop instead of multiple Loops of a coil I draw a single Loop and so current is moving from top bottom to top then I get the feel lines moving circularly around the loop moving in a circle around the loop and they stretch out at different points at the center of the loop right through the center it'll appear as a straight line but at other points it'll be stretched out in a circular shape and so we can use the right hand grip rule won't explain the right hand grip rule but that's since it's a lot simpler but the right hand grip row can be used to find basically if you grip all the fingers of your right hand and you extend your thumb as if you were showing thumbs up the curl of your fingers gives you the direction well if you're thinking about a current and your thumb uses the direction of the current and the curl of your fingers gives you the direction of the magnetic field and vice versa if you're looking at a solenoid the curl if your fingers gives you the direction of the current and your thumb tells you in which direction the magnetic field is and so this is for a flat Loop and in purple we have the field lines okay what's also important to remember here and I'm not going to go into this in detail is that if I take too long straight current carrying wires they feel a force okay and so if I were to draw the field lines again I would use the right hand grip rule to find the direction and so that's the field of the first wire let's assume the current is Flowing upward in both wires and we'd have the field looping in that direction and for the second wire we also have the current looping in a similar Direction and so at the point at which they meet we can see that the force on the wire to the left is pointing inward pointing to the right and the force for the wire on the right is pointing to the left and so we can use the left hand rule to find that and so what we notice is that like currents not like charges not like poles but like currents will attract each other so if you put two wires next to each other that have currents pointing in the same direction you have to be very careful the wires can short if they come too close to each other and then in the opposite direction if I have currents moving in the opposite direction then the force is at a pulsive one and so if one one of the currents is moving flowing upward and the others flowing downward then I have a repulsive Force so this is the opposite of thinking of electric charges or poles unlike currents repel and like currents attract piece of extra information because a question could rely on your ability to understand that principle okay now the next part also is fairly confusing or can get fairly confusing this topic really doesn't let up electromagnetic induction specifically Faraday's law but also the idea behind it so I'm first going to define something called the magnetic flux we spoke of the magnetic flux density we haven't spoke about the word flux now flux least in physics is simply the amount of something passing through something else passing through a region or an area and we give it this Greek symbol Phi the Greek letter Phi which is the flux density B multiplied by the area what does this mean that means if I have a region maybe a plane and the plane has an area a surface area a and I have the field lines pointing from some uniform magnetic field we will consider it all uniform for now at an angle Theta to the area or the normal Vector for the page the angle Theta means that the flux Phi is B times a times the sine of theta now we are only going to assume the case in which b and a are perpendicular and so Phi is simply b a sine Theta is one because theta equals to 90 degrees we're going to assume they always perpendicular just for the ease of understanding the units of measurement I use square brackets usually for units of measurement is Tesla meter squared and again we give it another derived unit which we call the Weber which is a uppercase W and a lowercase b be very careful about using symbols as units of measurement now why did I mention the magnetic flux because I want to mention another quantity now there's a lot of quantities here a lot to remember but bear with me it's something called a flux linkage it is n times Phi and this is B times a times n ban okay and again we're assuming b and a are perpendicular that's where the sine Theta disappears okay so what is this basically well think of think of it this way if I have a flat Loop of a coil then the surface area of this coil is a the field passes straight through the center of this coil B at its Center and so the flux passing to the one face Phi is B times a flux linkage is instead of having a solenoid one Loop which is not usually the case I usually have multiple Loops of coil if I have multiple Loops of coil then each of these has an area a and so the the magnetic flux Phi is B A Plus B A Plus well it's the sum of ba for the number of coils that I have if I have n loops n Loops of coil in the solenoid then Phi is simply b a n that's basically what I'm talking about n is to tell me the number of Loops I have in the coil simply why is that because I need to describe Faraday's law of electromagnetic induction now basically what does this say now I know again these are things that you may ignore when studying because it might be a bit overwhelming but simply Faraday's law of electromagnetic induction says one important thing uh changing magnetic field induces an EMF in a conductor very important point magnetic fields induce current magnetic fields induced emfs and so a changing meaning the magnetic field is constantly changing this induces an EMF in a conductor and so mathematically Faraday's law says that the EMF induced in a conductor when I place a magnetic field that's changing it's moving next to a conducting piece of wire the wire suddenly gets a magical current in it not so magical because mathematically this is the change Delta in the flux linkage which we already defined in Phi divided by the change in time is the EMF produced so simply says that change now it has to be a change in flux linkage in order for the EMF to exist so a change in flux linkage divided by a change in time gives me an EMF so the rate of change of magnetic flux linkage with a minus sign gives me the EMF produced in a conducting wire now this minus sign comes from something known as lenses law now you would have seen this as well and again it may have just frightened you a bit what is lens's law so basically lenses law says the direction of the induced EMF is such as to oppose the change that is producing it yes you may have memorized this definition as you should the direction of the induced EMF acts in a way to oppose the change producing it what does this mean let's assume I have a wire with a current placed next to a wire with no current Faraday's law says that the current or the EMF induces or the motor effect rather says that these this current induces a field we know that a current moving charge induces a magnetic field and so I have a nice circular magnetic field being produced around in a circular loop around this wire let's connect this wire to a power source so we know its power is not coming from anywhere power source resistor so we give power to this wire I place a wire next a second wire next to the first I'd bring it close to the first wire magic happens Faraday's law says a changing magnetic field if I can change the current in the first conductor and change the magnetic field or the flux density I induce a current or an EMF in the second wire now notice that one points up and the other points down that's what lenses law is telling us it says that the field of the first wire induces a current or actually an EMF to be more technically correct the EMF will eventually induce a current that opposes the original that's where the minus sign comes from in Faraday's law so this current that's induced will always be in the opposite direction and to the first and that's where the minus sign comes from this is to allow for the conservation of energy to stand you can imagine that if we have a current in One Direction generating a current in the same direction generating current this would be an effect that would just stack up and so energy would not be conserved and so this happens so as to cancel out the effects so that energy is conserved that's all that lenses law says and so if you think about the application of lenses law looking at some past exam questions especially now not that difficult any EMF that is induced or any field that is induced will oppose the original EMF or the original field that caused it and how does it cause it it caused it by Faraday's law of electromagnetic induction so I know this was fairly rushed and yes this is a long topic so it does require a lot of time and effort but I'm hoping that some of the concepts were that I explained here just made the topic a little bit easier that much easier to understand and like I said it is a very long topic with a lot of Concepts but I try to break them down as simply as I could to help you in answering questions so until next time I'm Mr K we'll see you soon on everything is relative