Fleming's left hand rule

in a previous video we saw that when you place a current-carrying wire inside a magnetic field that magnetic field can push on that wire it can put a force on that wire in this video we'll figure out the direction of this force acting on the wire so how do we do this well all we need to do is use Newton's third law Newton's third law says every action has equal and opposite reaction you see over here the wire is pushing on the magnets we can call that as action then the magnets push on the wire we call that as the reaction because the action and reaction forces are opposite in direction we will figure out in what direction the wire pushes on the magnets and then in the opposite direction the magnets will push on the wire so let's first figure out in what direction the wire pushes on the magnets well to do that lasker cells how does the wire push on the magnets well the wire creates its own magnetic field because of the current and it's that magnetic field that pushes on the magnets so let's remove this magnetic field and concentrate on the magnetic field generated by the wire we've seen before that the magnetic field due to a current carrying wire is in circles around it and the direction is given by the right-hand thumb rule where the thumb represents the direction of the current and the four fingers will represent the direction of the magnetic field so the magnetic field runs like this and just to recall what do we mean by magnetic field direction is this way it means that if I were to keep a tiny magnet over here it's not over experience a force to the right if I keep a tiny magnet here behind the wire its North Pole experience a force to the left so the direction of the magnetic field tells us in what direction the North Pole of a magnet kept Oh were there would experience a force now given this can we figure out in what direction this magnet and this pole needs to poles with experience of force so I want you to try to do this first and then we'll do it together all right let's do this to figure out the direction of the force on this pole of the magnet let's just concentrate on the field at this point can you see that the arrow mark is pointing out of the screen the field over here is pointing outwards that means the North Pole over there will experience a force outwards and since I have kept or not pull over there that North Pole must experience a force outwards so it's gonna be somewhat this way this way all right what about this Pole of the magnet again if you have not done this now be again great time to pause and see if you can do this Pole yourself all right let's see over here notice the arrow mark is pointing into the screen it's a little difficult to see but you have to understand that the field is running into the screen and then going behind the wire comes out of the screen and comes in front of the wire so since the arrow mark is pointing into the screen this means in North Pole over here would experience a force into the screen but we have kept a South Pole South Pole does the exact opposite thing of North Pole right and so if the North Pole experiences of words into the screen the South Pole would experience a force out of the screen oops so the South Pole would also experience both the poles of the magnet experience a force out of the screen and if this is a giant horseshoe magnet like shown over here then that means the whole magnet is experiencing a force out of the screen so the wire is pushing the magnet out of the screen and so from Newton's third law this means the magnet must push the wire into the screen so the force on the wire must be this way into the screen again it's a little difficult to see because drawing arrow marks into the screen is not all that easy but just visualize this and so that's how we can figure out the force on a current carrying wire placed in a magnetic field now I'm sure you agree with me that this is a pretty tedious method to first figure out the direction of the field generated by the wire then find the force on the magnets then use Newton's third law oh this is this is too much work right is there a shortcut to somehow just remember this so what I mean is if I go back to the original picture so we figured out the hard way that if the magnetic field is to the right and the current is upwards and the force on the wire is into the screen so my question is can we just remember this so that in the future we can solve problems very quickly rather than having to derive the whole thing again well it turns out there is a way to remember this and we can do that by using something called the Fleming's left hand rule so the Fleming's left hand rule says you bring in your left hand and you stretch your thumb forefinger and middle finger such that they're all mutually perpendicular to each other as you can see these two are perpendicular and these two are also perpendicular and even these two are perpendicular then the middle finger gives us the direction of the current the forefinger gives us the direction of the magnetic field then the thumb gives us the direction of the force acting on that current carrying wire all right so force magnetic field and current now for force we use F for magnetic field we use B the symbol for magnetic field is not M usually we use be and for current is I so the way I remember this is FBI okay FBI so let's see whether it works in this example in this example our magnetic field is to the right so this magnetic field FBI magnetic field is to the right our current is upwards so this finger has to go up okay there it is so my current is up and now notice the thumb is pointing downwards that is the force is into the screen exactly what we predicted from Newton's third law but anymore we don't have to use Newton's third law we'll just use this Fleming's left hand rule and do it so let's do one more Newman that's let's take one more kiss in this example the magnetic field is coming out of the screen it's not shown properly but imagine the magnetic field is coming out of the screen the current is to the right so can you use the left hand rule to figure out what is the direction of the force acting on the wire try it yourself first pause the video and see if you can do it yourself all right let's do this bring in our left hand stretch it this way f.b.eye so f is the force B is the magnetic field magnetic field is coming out of the screen so magnetic field is coming out of the screen like this the current is to the right current is to the right like this I'm finding it a little hard to move my hands so and that thumb will give us the direction of the force so the thumb as you can see is pointing downwards like this in this direction and so the force acting on the wire is downwards now one last question we might have is what if the magnetic field and the current are not perpendicular to each other like as shown in the figure over here what if there is some angle between the magnetic field and the current what happens then well it turns out the direction of the force won't change the direction of the force will remain exactly the same regardless of what angle we have between the magnetic field and the current so even if they are not at 90 degrees we can still use the Fleming's left hand rule but always the force will always be perpendicular to both these fingers that's the thing but these two need not be perpendicular to each other because it's our choice we can keep the current carrying wire at any angle with respect to the magnetic fields but don't worry too much about that in most cases that we will be dealing we'll always have them perpendicular to each other but it's not a necessity so what did we learn in this video we saw that to calculate the direction of the force on a current carrying wire kept in a magnetic field we can either use Newton's third law which is a little bit tedious or we can use the Fleming's left hand rule in which the forefinger uses the direction of the magnetic field the thumb uses the direction the middle finger uses the direction of the current then the thumb gives us the direction of the force acting on the wire and the way I like to remember it is force F magnetic field be current I FBI