today we're going to be revising the whole of electromagnetism now this is both an incredibly important a really interesting topic in a level physics and is naturally split into two sections first off we're going to have a look at magnetic fields which covers the magnetism part then we're going to be seeing how they relate to electric fields via faraday's law well let's have a look at magnetic fields initially so let's have a look at this fantastically drawn picture of the magnetic field around the earth the earth actually seems to act like a big bar magnet as if there was a big bar magnet on the inside of it notice how we have the north pole here and the south pole here so several very important rules become apparent once we look at a magnetic field the first one is the magnetic field lines always go from north to south from north to south for instance here is a magnetic field line it starts off from the north pole and you can see that it curves back into the south pole our second rule is that the arrow represents the direction at which a free north pole would move for instance if i had a free north pole around here this is still not been observed by the way a free north pole so if you were to find a free magnetic monopole what is called you'll probably be awarded a nobel prize but theoretically if we had a free north pole then that free north pole will spiral well not quite spiral but will follow this magnetic field line back to the south pole if we had equally spaced and parallel lines then this would indicate a uniform field for instance in this case i have some equally spaced parallel lines which would mean that over here would have a north pole somewhere like that and down here we would have a south pole with some uniform field between them there are several patterns that that we need to remember firstly if we had two opposing poles and the field pattern would be similar to this it can be approximated as being uniform between the poles but remember the field lines will always go from north to south if i had two opposing magnets or two opposing poles of magnets the field pattern would look like this remember the all of the field lines will be aiming to go towards the south pole so they essentially are going to be carrying on until they find a south pole along this direction okay guys up next is the magnetic field around a current carrying wire so remember the magnetic field around the current carrying wire let's say that we have a current i flying through this wire over here will be concentric circles this would be an excellent time to remind ourselves of this very important notation if i have a circle that has a cross remember this is like the back of an arrow and this would indicate that the current is going into the screen or into the page and if i had a circle with a little dot in the center this would indicate that the current is coming out of the screen or coming out of the page a very useful rule of thumb to remember is that if your current is going into the screen then the magnetic field around it will be concentric circle that will be going in the clockwise direction otherwise if we were to reverse the direction of the current so the current is coming out of the screen in other words for it to reverse the direction of this current then the magnetic field direction will also change and the current will now be going anti-clockwise another way of remembering this rule is via the right hand grip rule but just before we do that let's take a moment to appreciate my drawing over here this would be an excellent opportunity for you guys to smash that like button so the rule is that you imagine gripping a wire and then if your thumb points in the direction of conventional current then the curve of your fingers shows the direction of the magnetic field lines for instance if the current is going upwards we also have the thumb pointing upwards the field is then as you can see as we have drawn underneath follows the direction of the curve of the fingers so the magnetic field lines will be going in the same direction as the curve of the fingers a couple of common mistakes it's the right hand grip rule so this is really important you're going to get the opposite result if you use your left hand so you need to use the right hand additionally pay particular attention this is a conventional current and conventional current will be always be flowing from positive to negative we can make a little problem to actually test our understanding of the right hand grip rule for instance quite a typical problem would be simply to have a wire like so and just draw one wire let's say that the direction of the current is upwards i'm going to give you two points let's say a and b and a typical question might ask you to state the direction so state the direction of the magnetic field at let's say a and then b so at a and b the magnetic field will be following the right hand grip rule so you can imagine essentially gripping the wire with your right hand similar as shown over here and then you're gonna see that the field you're gonna have to imagine coming out of the screen and then going across from a to b and then into the screen at b so at point a the field will be coming out of the screen like so and that's the symbol that we tend to use that so out of the screen if you're doing this on paper it'll be out of the page and at b it will be into the screen like so so into the screen you could use those two rules to essentially draw out the field or the magnetic field around the solenoid please pay attention that the magnetic field are inside of the solenoid so in this region here can easily be assumed to be uniform this is really important assumed to be uniform like so the north pole is around here and then the south pole is here and notice the direction of the currents which will lead us to determining the direction of the north and the south pole so if the current is going downwards essentially right over here the north pole will be in this direction the field is going upwards the um the south pole will be here maybe the current switches direction the poles will also be reversed okay now it's time to look at the force on a current carrying wire so imagine that you have some sort of an external magnetic field of magnetic flux density it's called that magnetic flux density b some sort of a magnetic field uh which is this region over here and we also have a wire of length l inside of this field now if we have no current nothing will happen to the wire but if we were to have some current running through it i don't know maybe we put this wire in a circuit of some sort so maybe we have a little resistor like so and then we connect it to a little power supply like so now there's going to be current going from the positive to the negative terminal so there's going to be some current moving along here those electrons will start moving because there's going to be some current i that will be going through this wire the wire will actually experience a magnetic force and the magnitude of that force will be given by the following expression f is equal to bill sine theta now in this case f is the force b this is our magnetic flux density so let's write this down magnetic flux and density in a way this is a measure of the strength of the magnetic field and this is measured in the unit tesla i this is just our current our standard current which is measured in amps l is going to be the length of the wire so that's just the length of the wire measured in meters and theta and that we use the sine of sine of theta this angle here is the angle between the wire and the field so in this case we could say let's say that the the field is perpendicular to uh to the wire so for instance it could be let's say into the board or let's say that it's moving in this direction so there's a couple of very very important tricks with this equation first off when is this equation a maximum so f is equal to bill sine theta is max is a maximum when theta is equal to 90 degrees this is because sine of theta would then be equal to 1. and in your gcses you would have learned f is equal to bill that equation and this always assumes the field is perpendicular to the wire the uh force will be zero when theta is equal to zero degrees 360 etc in other words when the wire is parallel to the field there will be no force and this is really really important so now we know how to calculate the magnitude of the magnetic force using f is equal to build sine theta however we still don't know how to determine the direction of this force for instance we don't really know whether this arrow here is pointing upwards or whether this arrow here is pointing downwards how can we determine the direction at which the magnetic force acts well for that reason we need to revise fleming's left hand rule and once again let's take a moment to appreciate my drawing and hit that like button first off i know it sounds really obvious but it's really important that we use our left hand for this rule so we're going to use our left hand the force in our bill equation is given by our thumb so the thumb gives us the motion or the force on the wire our first finger also known as our index finger gives us the direction of the field and our second finger gives us the direction of the current for instance we could apply fleming's left hand rule to this example now what i want you to do now is to take your left hand then apply this remember the way we apply this to our problem is the following you're gonna have to try and imagine this in 3d the current is your second finger the field is your first finger so your first finger should now be pointing directly into the screen and if you do that you are going to see that your thumb will be pointing directly upwards which is the direction of the force that's acting onto this wire now that we have looked at fleming's left hand rule let's have a look at charged particles in a magnetic field so imagine that you have a positive charge such as this one you can see that it's positive once again and let's say that this positive charge enters a magnetic field now if the region of the magnetic field has or if the field direction is directed into the screen so the field is going into the screen we can apply fleming's left hand rule because this is a positive charge the direction of current will be from positive to negative in this case this will be to the right so the current is going to the right the field is going into the screen so if we apply fleming's left hand rule there's going to be a force which will be acting upwards but hang on a minute this positive charge is already going to the right and if the charge was initially going to the right and suddenly we have a force which is acting at 90 degrees well this would actually be a centripetal force remember centripetal force will be always be acting at 90 degrees to the direction of motion and the force and the motion will always be perpendicular to always be pointing towards the center so what will happen to this charge is that it will actually start to curve within the region of that magnetic field the reason why it starts to curve is because the magnetic force is acting as a centripetal force so we can set the two uh equal to one another we can say that mv squared over r which is our centripetal force is going to equal to bill which is our magnetic force so what we can do now is rearrange for our radius of curvature so what we're going to do is first of all use a slightly different or modify a little bit our bill equation so let's just do that up here because we know that f is equal to bill then because our current is defined as the rate of flow of charge so it's going to be q divided by t multiplied by l we know that l over t will is actually our velocity so this is equal to b q multiplied by v we often write this as q e v b which is another expression for the uh magnetic force that's acting on a single charge okay well let's write this in here so mv squared over r will be equal to qvb and what i'm going to do now is i'm going to rearrange for the radius first off we can cancel out one of those v so what we're left with is that m v is equal to q b and i'm going to bring the r across like so finally i'm going to rearrange for the radius and this will be equal to m v divided by q b and this is a formula that you guys need to remember how to derive in the exam remember anytime you have a charge which is essentially moving in a circle in a magnetic field we could set the magnetic force qvb equal to mv squared over r remember there are two formulas for the magnetic force one is that f is equal to bill the other one is that f is equal to qvb and then we could easily go from one to the other okay next up for revision is magnetic flux now magnetic flux is the product of the magnetic flux density perpendicular to an area and the area itself so remember magnetic flux density so i'm just going to underline that here this quantity is just b so what we need to find is the component of the magnetic flux density perpendicular to an area in other words it's going to be just this component over here like so so let's say that the angle here is theta the component which is perpendicular to the area will be given by the adjacent component so this will be cosine theta in other words b cosine theta the magnetic flux is given this greek letter phi and the magnetic flux is defined as the product of the magnetic flux density which we said was b cosine theta let's write this a little bit more clearly so b cosine theta multiplied by the area itself which is a now this is commonly written as phi is equal to b a cosine theta and this is really really important that theta is the angle between the field lines and the normal and this is so important that i'm even going to write this down so theta is the angle between the field line and the normal so quite a common mistake would be for people to indicate that theta is this angle here this is not true it is the angle to the normal because our equation is that the magnetic flux is equal to b a cosine theta we're going to have maximum magnetic flux when the field is perpendicular to the area so in this case the field is perpendicular to the area and here the field is parallel to the area which will be leading to zero magnetic flux mathematically speaking we could use the fact that here the angle between the normal and the field lines is zero remember theta is the angle between the field lines and the normal and here they are parallel so in this case phi will be equal to ba times the cosine of zero degrees which is equal to ba so our magnetic flux will be equal to b multiplied by a in this case though the field line is parallel to the area which means that it's perpendicular to the normal so remember in our equation phi is equal to b a cosine of theta theta is the angle between the normal and the field lines in this case it's equal to 90 degrees so phi our magnetic flux will be equal to ba cosine of 90 degrees and cosine of 90 degrees is zero which means that our magnetic flux will be equal to zero we can test our understanding of this question with this really simple uh example here find the magnetic flux through this this area if the magnetic flux density is three milli teslas and you're given the various different dimensions for the area okay well let's do that so we're looking for the magnetic flux so we're going to use phi is equal to b a cosine of theta now the first thing i'm going to do is just draw the normal and all of these problems which is like so so if the angle here is 55 so the whole thing is 90 which means that this angle here has to be 35 degrees okay well let's do some calculations b our magnetic flux density is three milli tesla so that's three times ten power minus three our area is three centimeters by five centimeters so it's going to be three centimeters is three times ten about minus 2 multiplied by 5 times 10 to the power minus 2 multiplied so this together is our area multiplied by the cosine of 35 degrees putting that into a calculator we are going to get 3.7 times 10 to the power of -6 weber's by the way just a quick reminder about units the unit for magnetic flux density b is the tesla and the unit for phi the magnetic flux is the weber it's always good practice when revising to work out some base units so for instance let's work out the base unit for magnetic flux density so i'm going to write down an equation for it so i'm going to write f is equal to bill sine theta i'm going to assume that theta is um equal to 90 degrees so sine of theta will be equal to one so i'm just going to be using f is equal to bill okay well first off let's rearrange for b so b will be equal to f divided by i l now our force is in general equal to mass times acceleration divided by a times l okay well let's think about the units of this quantity so meters let's draw some hours actually from the individual units so meters oh sorry mass of course is given in kilograms acceleration will be given in meters s to the power of minus two we're going to be dividing that by the units of current remember current is a the amp is the base unit it's also the it's a standard unit for current is the base unit so that's the base unit for the current and of course a meter is the unit for the length so those guys can cancel out and what we're left with is kg a to a power of minus 1 s to a power of -2 for the base unit of the magnetic flux density now because phi of magnetic flux is equal to a cos theta the cosine is unit less so the base unit for the magnetic flux will be equal to the base unit of b which is kg a to power of minus 1 s to a power of minus 2 so that's the base unit of b multiplied by the base unit of area which is meters squared i'm going to also define one more quantity and this is known as magnetic flux linkage so let's just write this down magnetic flux linkage and this is given by the expression of n multiplied by our magnetic flux phi and in this case is literally the number of coils so it's the number of coils let's have a look at an example so now we're starting to delve properly into electro early to electromagnetism so far we've mainly been looking at some maths and maybe been looking at uh magnetism and we've done a lot of work as you can see we've done all of this well let's have a look at faraday's law now michael faraday had this absolute stroke of brilliance when he discovered his law faraday's law so far we've looked how if we have electric current that can make a force arise onto a conductor what faraday did was with the reverse what he did was he moved a magnet and hence changed the magnetic field in the presence of a conductor and this in this case this is a copper wire let's say this copper wire has n loops or n coils what he discovered to his amazement that there was an induced emf so actually the movement of the magnet was inducing a current within the wire if you think about it faraday really has discovered the generator which is been incredibly important to essentially the development of civilization over the um over the last couple hundred years now faraday's law says that the magnitude of the induced emf is directly proportional to the rate of change of magnetic flux linkage mathematically we we express this as so so e is equal to minus delta n phi over delta t we could also write this as minus delta n be a cos theta remember uh phi or magnetic flux is actually equal to b a cos theta then i can also then also need to divide that by our change of time because in physics anytime we have the rate of change of something we're dividing by delta t the minus sign here is actually really really significant and this minus sign is an expression of lenses law lenses law actually states and this is really important i'm going to circle it over here the the direction of the induced current is such as to oppose the change producing it now what do i mean by this for instance if i have a north pole of of a of the magnet which is approaching this uh this copper wire then the the wire will turn itself into a magnet and the current will be such so that the the the wire which is now an electromagnet will produce a north pole which will be repelling this north pole so lenses law means that uh the two north poles will will repel and this is actually a statement of the law of energy conservation because if they didn't repel what would happen was if we moved it towards it let's say this turned into a south pole then the magnet will just fly through and energy will not be conserved i have an extremely detailed video on this and because this is a revision video i'm not going to go into as much detail but feel free to have a browse in the description you're going to find a link to that video now that we have had a really good look at magnetic flux and also faraday's law let's have a brief look into the ac generator so imagine that we have a coil which i've placed in a magnetic field the magnetic field has the following direction so this here is our b field that i've drawn in red if our coil is being rotated as follows so you can imagine that it starts up here and then a moment later it's being rotated this way and then a moment later it's rotated this way so now it's flat and then we have it perpendicular to the field yet again well let's think about the angle of the normal to the field so the normal is along here so initially we have theta is equal to zero now remember n phi is equal to nba cosine of theta so cosine of zero is one so we can have our maximum flux right over here and this is why a graph of the flux linkage like so against time for the ac generator will look like so initially our flux linkage is at a maximum and then we'll be steadily decreasing until the moment when our coil is now parallel to the field lines now in this case our normal is here and our field is along there which means that theta is equal to 90 degrees and cosine of theta in this case will be cosine of 90 which is equal to zero therefore our flux linkage will be zero and this corresponds to this point over here afterwards theta will be equal to 180 degrees and cosine of 180 is -1 so this will be this point over here and the whole process will be repeating itself and we'll be producing current which is constantly changing direction as our coil is moving and to this day this is the method behind producing electrical current talking about this graph by the way it's really really important to have a look at the y equals mx plus c analysis now remember faraday's law says that our induced emf is equal to minus n phi or the rate of change of n phi divided by delta t so our gradient this is really important the gradient of this curve the gradient of the graph will give us the magnitude of the induced emf so it'll be to give us the magnitude of the induced emf and our final topic of electromagnetism is transformers okay well how does a transformer actually work first off we're going to have a soft iron core or just an iron core and then what we're going to need is some primary voltage so we're going to take a wire then we're going to loop it around one of the ends like so and this will be connected to a variable power supply that produces some ac current which is absolutely crucial so we want this to be connected to an ac power supply so let's just write that so afterwards we are going to have a secondary coil which will be along here like so that we could maybe just connect let's say to an oscilloscope or to a voltmeter uh on to the other side so we can draw in a voltmeter along here okay well how does a transformer actually work first off whenever we have ac current we have current which is continuously changing direction over 50 times a second the current's going this way this way this way this way continuously changing direction when that happens the magnetic flux linkage that's being created by the electrical current that is changing direction is also changing now how about a minute now suddenly i have changing flux around this area over here which is going to induce an emf into my secondary coil i have summarized how transformer works over here first off ac current as we said produces a rate of change of magnetic flux linkage the soft iron core by the way is here to to link the primary core to the secondary one it's kind of providing an easy path for the magnetic field lines to to follow so the emf is induced in the secondary coil by faraday's law it's important to know that there's no actual proper physical connection between the currents in the primary coil and just label them that this here is the primary coil and this here is the secondary coil but emf is induced in the secondary coil by faraday's law because the first coil is producing a magnetic field and that magnetic field is changing which changes the magnetic flux which of course produces a rate of change of magnetic flux which induces emf in the secondary coil and finally let's have a look at the equation that we have for transformers now our equation for transformers says that ns over np is equal to vs over vp in this case ns is the number of turns in our secondary coil and p is the number of turns in our primary coil and vs and vp are the respective voltages in the two coils the current is kind of flipped in this equation so vs over v p will actually be equal to i p over i s this is kind of important or pretty important well why is that this is all to do with power conservation so the power in the primary so p subscript p will have to be equal to the power in the secondary because power is equal to v i we can say that v p multiplied by i p will be equal to v s multiplied by i s so what we can do is just simply rearrange for v s over v p so v s over v p will be equal to i p over i s so if you're wondering where this part of the equation comes from it's from right there okay folks well we've actually covered virtually all of the points of this very very vast topic of electromagnetism well done for revising good luck with your revision and good luck with your exams thank you very much for watching and i hope this video was useful