Let There Be Light: Maxwell's Equation EXPLAINED for BEGINNERS

it is my fundamental belief that there are many complicated physics concepts that can be explained to someone with just a basic understanding of high school physics and mathematics and this video is my attempt at explaining Maxwell's equations or at least one of them so first of all why am I making this video well last week I did a poll on Instagram asking you guys what video you wanted to see first video on Maxwell's equations or a video about the structure of the atom Maxwell's equations one out so here we are thank you so much if you voted in the poll and if you're not already following me on instagram then please head over there and follow me I post one minute long physics videos as well as just random stuff I'm doing throughout the day on my stories and follow me on Twitter if you want to hear the worst physics puns you've ever heard in your life anyway let's get into the video Maxwell's equations are a set of four equations that brilliantly describe electricity and magnetism collectively this is known as electromagnetism they are complicated and intricate so probably deserve about 10 videos to be dedicated to them so to do justice to Maxwell's equations in this video I won't be focusing on all four of them I'll just be focusing on one of them this one so let's get straight into it what do these symbols even mean well like I've already said Maxwell's equations focus on electricity and magnetism now B in this case represents the magnetic field that we're studying why do we use the letter B to represent a magnetic field yeah don't even ask don't ask the downward pointing triangle and the dot next to it together represent something known as divergence so what is divergence right here we go well the divergence is often applied to something known as a vector field okay part now you're just saying words what the hell is a vector field guys trust me bear with me here it all makes sense very shortly now to understand divergence properly first we need to understand what a vector field actually is so a vector field can be thought of as a region of space where we can assign a vector or an arrow pointing in a certain direction to every point in that region of space like I said already by the way a vector is just an arrow with a particular size and pointing in a particular direction this vector can be used to represent something in the vector field a classic example is a vector field showing the direction and speed of wind on a weather map a lot of us have seen these on TV for example where the vectors assigned to every point in this region basically show us the direction and speed of wind so for example at this point the wind is blowing really hard to the east and at this point the wind is blowing softly to the south the laws of the vector the higher the wind speed and the direction shows the direction of the wind so this overall is a vector field is basically a field of vectors the vectors represent something in this case the speed of the wind now guys before I continue if my explanation of a vector field is not clear enough then let me know in the comments down below I've got a couple more examples coming for you guys that should hopefully clear it up but also if there's anything in this video that isn't quite clear then let me know in the comments down below as well and I'm going to be cheeky here if you're enjoying the video so far then please leave a thumbs up but let's get back to it here's another example of a vector field coming back to electromagnetism a classic example of a vector field is the magnetic field around a bar magnet we've often seen these in high school especially demonstrated with a bar magnet and iron filings the iron filings are easily magnetized and so follow the magnetic field around the bar magnet because the bar magnets magnetic field exerts a force on each one of these little iron filings and the magnetic field lines that we draw basically show the direction of force on these iron filings so yes a magnetic field can be represented as a vector field where this time a vector in the vector field represents the direction and size of the force experienced by a magnetic object placed in the magnetic field so now that we know that a magnetic field around a magnetic object can be represented as a vector field let's go back to looking at the divergence of a vector field and what that means well when we're trying to find the divergence of a vector field essentially what we do is we choose a small region of space within that field and we see how much that vector field either points into that region or out of that region again this is fairly confusing so let's use an example to demonstrate once again let's put a side magnetic field and let's consider another vector field this time I want you to close your eyes and imagine you're drawing yourself a relaxing bath because obviously there's no better place to do physics no but seriously imagine that you're running yourself a bath in a bath that has taps at one end and the drain at the other end now this is fairly uncommon I know that usually the drainers are the same side as the taps but for demonstration purposes let's imagine that they're on opposite ends of the bathtub now let's say that in this case you've forgotten to plug the drain so you're doing a really bad job of drawing yourself a bath because the water flows into the bathtub from the taps and flows right back out from the drain now at this point you're obviously wasting water and damaging the environment but it's okay because it's for the sake of physics and because it's only in your head now let's say that we're looking at the bathtub from above we can represent the flow of water on the floor of the bathtub with a vector field we know that at the tap end of the bath the water is flowing down onto the floor of the bath and they're spreading outwards in the middle region of the bathtub water is flowing away from the tap end and towards the drain end and at the drain end all of the water is flowing into the drain and down the plughole now of course it's important to realize that this is only the net or overall flow of the water because of course some of the water will reflect of the size of the bath and be flowing in all different directions but overall the water is flowing away from the tap end and towards the drain end now let's say that the vector field at any point is represented by the vector V V standing for velocity unlike be standing for magnetic field apparently but of course because the vectors are different at every point along the bathtub floor sometimes they're large sometimes they're sure sometimes they point towards the right sometimes towards the left V obviously changes at every point okay so now that we have a vector field which represents the velocity of the water on the bathtub floor let's take the divergence of the vector field let's start then with a middle region of the bathtub floor when we're taking the divergence we look at the vector field flowing into that circle and out of that circle in this case water is flowing into the circle from the left and is flowing straight out to the right in other words if we take the divergence of V in this region then we say that it's divergence is zero because and here's the thing this means that overall there's no flow into the circle or out of the circle but hang on on all regions in the vector field like that where water flows in and flow straight back out again the other side now PHAB check this out let's say we now take our divergence at the tap end of the bathtub floor now if we place our circle here then clearly water is flowing out in all directions there overall there is a net flow of water outwards from our divergence circle now because water is all flowing outwards that means that this is a source of the water and this is fairly common terminology if the vector field is overall flowing outwards from your region then that region is known as a source of the vector field and more importantly this region is said to have a positive divergence in other words the divergence of the vector field V in this region is positive now conversely we can take our divergence at the other end of the bathtub floor this time at the drain end and we can clearly see in this region that all of the water is flowing in towards our circle this kind of region where overall the vector field is flowing into our region is known as a sink and a sea of the vector field is said to have a negative divergence and so that is how the divergence of a vector field works in a relatively intuitive way of course there's a little bit more mathematical subtlety and intricacy to it but that's not really important to us right now so let's get back to Maxwell's equation that talks about the divergence of the magnetic field now this equation tells us that the divergence of the magnetic field is zero always because it's not saying that in some specific regions of divergence of the magnetic field is zero no it's saying that the divergence of any magnetic field of any magnetic object is always zero this is really important because it tells us a couple of things firstly it tells us that there are no individual sources or sinks of magnetic field compare this with electric fields by the way which has sources and sinks positive charges are sources because the electric field goes outwards from a positive charge and negative charges are sinks because the electric field points inwards towards a negative charge this is not true for magnetic fields according to Maxwell's equation so let's check this is true for the simple case of a bar magnet let's see if we can find any sources or sinks of the magnetic field on this diagram is there any region that we can draw where overall the magnetic field is either flowing in or flowing out well let's start with this region just a random region in the magnetic field look magnetic field flows in and then it flows straight back out again so the divergence in this region is zero but what about the poles of the magnet this looks fairly promising because if we draw a sphere around the North Pole of the magnet for example then we can clearly see that magnetic field is only flowing out of the sphere there's nothing flowing back in it's a source right well no not really the only reason it looks like a source is because we haven't drawn the magnetic field lines inside of the bar magnet but when we do it looks like this and there you go magnetic field now flowing in and flowing straight back out again from this we can deduce something really important Maxwell's equation is telling us that there's no such thing as a magnetic monopole or single individual Pole you can't just have a North Pole by itself which gives out a magnetic field and you can't just have a South Pole by itself either whenever you have a magnetic substance that substance will always have a north and a South Pole this is why when you chop a bar magnet in half you don't just get a separate North Pole and a South Pole you now get two little bar magnets each of which has a North Pole and a South Pole of its own however interestingly there are some modern theories that predict the existence of magnetic monopoles so scientists have been on the search for the existence of these mono poles for well now no evidence has been found as of now as of when I'm recording this video there's even an episode of The Big Bang Theory where Sheldon develops a theory that predicts the existence of magnetic monopoles to search for evidence of this the guys go on an expedition I think to the Antarctic and spoiler alert in the next episode they come back supposedly successful they think they found evidence for the magnetic monopole and this is a huge deal because it means the Maxwell's equation is wrong and therefore this evidence has started a new era in physics so getting back to Maxwell's equations you see what I mean about them being really complicated and intricate this video has gone on long enough and I've only discussed one of the four equations the equation that we discussed was probably one of the simpler ones to explain and it's taken me this long ass video to do it so if you liked this video and found it useful then please leave a thumbs up I really do appreciate it but now it's time for the weekly question of the week my weekly question of the week for you this week is what is your favorite thing about physics it can be a particular area of physics or it can be anything about physics as well like the fact that it's evidence-based and it's probably the best thing that we have in trying to understand how our universe works also comment down below if you want me to do another video covering another one of Maxwell's equations and yeah if there's something that I haven't made quite clear enough then let me know down below and if I've made a mistake then feel free to blast me down the comments as well subscribe if you haven't already for more physics content I make fun physics videos that I don't have to try too hard cuz physics is already fun and hit that Bell button to be notified every time I upload okay now that all the YouTube you stuff is out the way guys thank you so much for watching I really appreciate it and I will see you next time buh buh buh buh bye [Music]

Channel: Parth G

Views: 439,410

Rating: 4.9631743 out of 5

Keywords: Maxwell's Equations, Electromagnetism, Divergence, Vector Field, Physics, Maxwell's Equations Explained, Maxwell's Extension to Ampere's Law, Science, Magnetic Field, Physics for Beginners, Physics for noobs, Let There Be Light

Id: 0jW74lrpeM0

Length: 10min 38sec (638 seconds)

Published: Tue Feb 19 2019