Right hand thumb rule (& solved numerical)

in a previous video we saw that a straight wire carrying an electric current produces a magnetic field in concentric circles around it in this video we're going to see how to remember the direction of the magnetic field due to the current so let's say this pen represents our straight wire carrying an electric current and let's say the current is running this way towards the tip of the pen then we know the magnetic field around it will be in circles but that can be in two directions if I use a bangle to represent the magnetic field then it can either be this way where on the top the magnetic field is to the right as you can see by the arrow mark or it can be this way we're on the top the magnetic field will be towards the left so how do we remember what direction is going to be is the question so a simple rule that we're going to use over here is called the right hand thumb rule it says that you take your wire and you clasp it with your right hand not the left hand right hand such that the thumb represents the direction of the electric current so we're here notice the electric current is this way so my thumb has to point in that direction then the four and circling fingers will tell us the direction of the magnetic field so over here notice the encircling fingers are telling me that a magnetic field on the top is to the right and so now I know that the magnetic field has to be this way says that on the top it's to the right and if the electric current were to reverse let's say downwards electric current was downwards now I would clasp the same conductor with my right hand this way because the thumb should point in the direction of the current this way and so now look at the four fingers the four fingers are telling me that the magnetic field on the top is to the left can you see that it's to the left and therefore now the magnetic field magnetic field is going to be this way sometimes you have to figure out the direction of the magnetic field at a specific point around a conductor for example again let's say we have a current carrying wire which is carrying current in this direction and I ask you what is the direction of the magnetic field at a specific point over here to the right of the conductor how do we calculate that well again the first step is the same you use your right hand clasp rule and figure out the direction of the magnetic field line it's gonna be this way so it's gonna be to the right on the top and I use my bangle again like this and once you have the magnetic field line to figure out the magnetic field at a specific point you just draw a tangent to the field line so I want to find out what is the magnetic field at this point to the right side I'm gonna hold the conductor this way so I can hold it all right so I want to know what is the magnetic field at this point over here so you have to imagine it tangent to this circle at this point what would that look like well I'm just gonna tilt a little bit so that you can see properly if you draw a tangent over here not as you can do two tangents one this way one this way but since we already know the magnetic field is gonna run like this the tangent has to be downwards so the magnetic field to the right of the conductor is going to be downwards like this over here I could have just rotated this bangle also and notice when I come to this point hopefully you can see the arrow mark points downwards so what would be what do you think would be the magnetic field Direction at the bottom can you try and do this yourself now think about this pause the video and think about this at the bottom over here at the bottom well again finally it's a little hard to hold again I'm gonna hold it this way fine so if you come right at the bottom again imagine drawing a tangent here what would the tangent look like well tilt a little bit so you can see the tangent might be this way or this way but again since I know the magnetic field runs like this the tangent has to be in this direction again I could have just rotated that notice you can actually see the arrow mark at the bottom it's in this direction now calculating doing it this way it's it's fine if you have a prop with you like if you have a bangle and you have an arrow mark attached to it but what if you don't have access to it imagining this could be very difficult at least it used to be difficult for me so I'll tell you what I used to do when I didn't have any props so again first step class believe the right hand same steps now I imagine the magnetic field running like this so you also try and imagine this magnetic field is running this way now instead of a prop I'm going to use my finger as an arrow mark and I'm going to run in the direction of the magnetic field like this run in the direction and now if I want to know the magnetic field at a specific point I'll just stop over there so for example if I want to know what's the magnetic field direction at the right side I'm just gonna stop and notice it points downwards if I want to know what's the magnetic field at the bottom you're gonna stop hey it's to the left if I wonder was the magnetic field to the left of it it's upwards and so on and so that's how using the right hand clasp rule and then running your finger along that field line you can figure out the direction of the magnetic field at any point so let's solve a couple of new miracles now a wire carries an electric current from west to east find the direction of the magnetic field at a point directly below the wire okay so here we have to use east-west north-south so just to remember this is north this is south right is east left is west up and down so we have a wire that carries electric current that runs vest to east so vest to east is this way if this is our wire from west to east electric current is in this direction we need to find the direction of the magnetic field at a point directly below the wire so we have to find somewhere below it so pause the video and see if you can try it with yourself first alright let's do this so first step is to use your right hand and clasp this conductor this way the thumb should point in the direction of the electric current so it's going to be this way and so the four fingers are telling me the magnetic field runs in this direction I'm not going to use any props now let's all let's let's just imagine this and so the magnetic field runs like this this way and so I'm going to use my fingers to represent that and since I want to know the magnetic field below the wire I'm gonna stop below the wire now this way and so below the wire the magnetic field is to the north this is not up this is up this is to the north so the answer is to the north alright let's solve one more suppose you are standing in your room and you find an electron moving from the ceiling to the floor right in front of you find the direction of the magnetic field towards your right all right let's think about this I'm standing in my room over here and there's an electron that's moving from the ceiling to the floor like this and I need to find out what direction is the magnetic field to my right side to my right side over here now you may be wondering where is an electron come from well remember an electron is a charged particle and whenever charged particle moves it creates a current and we know that current produces a magnetic field and that's how there's a magnetic field and we need to figure out what direction the magnetic field is on the right side on my right side so this is a little bit tricky because electron is a negative charge so again pause the video and see if we can figure this out alright the tricky part is electrons are negatively charged particles so if electron is moving downwards a negative charge is moving downwards then the direction of the current is upwards because you may remember electric current Direction is a direction of positive charge opposite direction of negative charge so since electron is moving down our current would be upwards like this okay that's the only tricky part and now we have to figure out the direction of the magnetic field over here alright so if you've not done it before now would be a great time to again pause and see if you can figure it out all right first step is to use the right hand to clasp this conductor such that the thumb points in the direction of the current and now the four fingers will tell me what direction the magnetic field is and so it's telling me the magnetic field runs this way like this and so I'm going to use my finger to run it like this magnetic field runs this way since I want to find the direction on the right side I'm going to stop on the right and it's gonna be this way and so that is towards my north so the magnetic field over here is to the north so what did we learn in this video we learned how to use the right-hand thumb rule to give us the direction of the magnetic field basically whenever you have a current-carrying conductor you use your right hand thumb right hand clasp it says that the thumb uses the direction thumb represent the direction of the current and then the four fingers will tell you what direction the magnetic field is