in this video we're going to focus on faraday's law of electromagnetic induction so let's take an iron bar and we're going to wrap some coils of wire around it so here we're going to attach this to a voltmeter and on the other side we're going to have some coils of wire and we're going to connect this side to let's say a battery and we're going to have a resistor so there's not too much current flowing through this circuit now when is a steady current flowing in this circuit no emf no current is induced in the second coil now let's say if we have a switch the moment when we close the switch for an instant for a very short period of time we will get an induced current in that circuit the question is why why is it that when the current is steady it induces no current in the second coil however the moment that the current increases for that brief period of time when the current is changing there is an induced emf in the second coil and that's the basis of faraday's law of electromagnetic induction a change in magnetic field will give rise to an induced current now the equation that is associated with the faraday's law of electromagnetic induction is this formula the induced emf is equal to negative n times the change in the flux divided by the change in time so the faster the flux changes that is the magnetic flux the greater the induced emf will be in the second coil a change in magnetic field leads to a change in the magnetic flux which will give rise to an induced emf the magnetic flux is equal to the magnetic field times the area times cosine theta where theta is between the normal line perpendicular to the face of the coil and the magnetic field itself so there's three ways in which you can induce an emf in order to acquire a change in flux you can either change the magnetic field you could change the area of the coil or you could change the angle of the magnetic field with respect to the normal line of the coil so for example let's say if we have a square coil of wire and we want to take a magnet and we're going to move this magnet into this coil as we move the magnet into the coil the magnetic field is increasing and so this leads to an increase in the flux that's going into the coil and that's going to cause an induced emf so that's one way in which you could change the flux going into the coil is by changing the magnetic field by moving a magnet into or out of the coil if the magnet is held in place no induced current flows because there's no change in magnetic flux but as the magnet moves either into the coil or out of the coil there is a change in the magnetic field which leads to a change in the magnetic flux in the coil and then therefore there's going to be an induced emf that is going to lead to an induced current we're not going to focus on the direction of the current in this video but i just want to give you a basic introduction into faraday's law of induction so far we've seen one way in which we can induce a current in a coil by moving a magnet into or out of the coil now what are some other ways how can we change the area well let's say if we have a magnetic field actually let me draw the coil first so let's say we have a circular coil of wire and everywhere we have a magnetic field going into the page and so this magnetic field is constant doesn't change now what's going to happen if we basically pull the coil in such a way to increase the area of the coil if the area goes up the magnetic flux will increase and if the magnetic flux changes this would lead to an induced emf in the circuit so there's going to be an induced current in the circuit so that's the second way the third way is to change the angle with respect to let's say the magnetic field so let's say if we have a square coil of wire and let's say the magnetic field is directed into the page if we rotate this coil in this direction then we're going to change the flux because we're changing the angle right now the angle is 90 degrees but with respect to the normal line it's zero degrees it all depends on how you define it so let's define it with respect to the normal line so the magnetic field is parallel to the normal line right now and let's rotate the coil so it's like this now and so this is the normal line well actually it should be more like that and let's say this is the magnetic field clearly the angle is a lot different now it's no longer 0 degrees it might be i'm just going to give a number 70 degrees or something and so because the angle changes the magnetic flux will change in fact going from zero degrees to 70 cosine zero is the one cosine seven is a lot less so the magnetic flux decreased which means that there's going to be an induced emf in this coil so those are the three ways in which you can generate an induced current in the coil you can change the magnetic field you can increase it or decrease it doesn't matter you could change the area of the coil by stretching it or compressing it or you could change the angle between the magnetic field and a normal line if you change the angle then the flux changes and there's going to be an induced emf in the coil now let's work on a practice problem so we have a square coil of wire and that wire consists of 50 loops and we're given the dimensions of the square now there's a magnetic field that's perpendicular to the face of the coil so let's draw a picture so let's say this is the coil and let's say the magnetic field is going straight into it it's perpendicular to the face the coil but it's parallel to the normal line which means the angle between the normal line and the magnetic field is zero degrees now the magnetic field increases from negative three tesla to five tesla now this coil is connected across a resistor how can we calculate the induced emf in the coil and the current that flows through the resistor so let's focus on the induced emf so it's going to equal negative n times the change in the magnetic flux divided by the change in time so the change in magnetic flux in this example we know flux is going to be ba cosine but what is changing in this example is it the magnetic field the area or the coil well we know based on the problem the magnetic field is changing the area is constant and the angle is constant so we could say it's delta b because that's changing times a it doesn't need a triangle because that's not changing times cosine theta divided by the change in time so now let's plug in everything into this formula so n is 50 the change in the magnetic field the final value is five minus the initial value of negative three now the area is point twenty times point twenty twenty centimeters is point two meters multiplied by cosine of 0 degrees divided by the change in time so the change in time is 10 seconds i mean that's 10 seconds 0.1 seconds so 5 minus negative three that's the same as five plus three that's eight so it's negative fifty times eight times point two times another point two times cosine zero which doesn't change anything divided by point one so in this example well first i need to make some more space the induced emf is negative 160 volts now for this video i'm not going to worry about the negative sign so if we wish to calculate the current it's going to be the induced emf divided by the resistance and we know the resistance in this example it's 20 ohms so 160 let's just make that positive divided by 20 ohms is equal to 8. so that's the current that flows in this circuit it's 8 amps now the last thing we need to do is calculate the power dissipated by the resistor so the power absorbed by the resistor we can use this formula it's i squared times r so 8 squared times the resistance of 20 ohms 8 squared is 64 64 times 20 that's equal to 1280 watts and so a lot of power can be generated by a change in magnetic field or a change in flux in the coil of water and the more coils or rather the more loops that you have the greater the induce emf because if we had a single loop the induced voltage won't be this high it would be 160 divided by 50 and so it would only be 3.2 volts but if you increase the number of loops the induced emf greatly increases which is what you want you