 We are surrounded by electromagnetic waves, from a mobile phone to an x-ray revealing a broken bone, to the beauty of a sunset. All involve electromagnetic waves. In this video we will explore how these electromagnetic waves are created, and how do they travel or propagate in all directions. Here we have a stationary positive charge, and we can see the electric field lines coming out of it going in all directions. I have not marked the arrows, but since this is a positive charge, the electric field lines are going away from the charge in all the directions. When the charge is stationary, we see no disturbance in the electric field lines. The electric field lines go radially outwards, and there is no sign of any electromagnetic wave whatsoever. Now let's try and accelerate this charge downwards for a small time interval, and try to understand the effect of this acceleration on the electric field lines. So after some time the charge could be right over here. Now it seems that the electric field lines, they should look like this. They should go along with the charge. Because after all they are coming out of the charge, but it turns out that the information or the message that the charge has accelerated does not travel with an infinite speed. So the electric field lines far away from the charge might not have even received the message that the charge has accelerated. The message or the information travels at a finite speed, and let's say for example that it travels with a speed of 10 meter per second. In reality it travels with a speed of light that is 3 into 10 to the power 8 meters per second, but just for a sake of understanding about what's really going on here, let's say it travels at the speed of 10 meters per second. So that means that the message that the charge has accelerated, it must have reached all the points at a distance of 10 meters from the charge. And this looks like a circle, but it is actually a sphere. So the electric field lines within this region, this sphere, they accelerated with the charge. They remain stuck to it, but the field far away outside this sphere of 10 meters radius has no idea that the charge has accelerated. So the electric field outside this sphere is exactly the same when the charge was when the charge was in its initial or original position. It is still in the old state. Let's see how that would look like. So we start from the original position and we accelerate the charge downwards quickly. So let's do that. Whoa! So what do we see over here? The field near the charge accelerates with the charge, but the field far away doesn't because the information of acceleration hasn't even reached them. But these field lines near the charge, they must meet the field lines at the old state because they are the same field lines after all. The electric field lines cannot break. So the field between these distances, between these distances, they must join. This leads to the formation of kinks. They look like this. There is a kink form here, here and here, but none is formed along the axis of movement. None is formed vertically. It is this kink or collection of kinks which is responsible for electromagnetic radiation that we will see in a while. And these kinks, they move outward with a speed of light. So let's see how that would look like with the help of an animation. So here we have the same positive charge and this will be accelerated downwards quickly. So when we do that, notice how these kinks move outwards. Let's look at this again and there you go. Alright now accelerating charges, they produce kinks and these kinks, they move outwards with a speed of light. Now in order to understand how these kinks might be responsible for electromagnetic radiation, we need to look closely at this region of electric field. Here we have the same charge accelerating downwards. So when it is further down, it has some acceleration and also some velocity due to that acceleration. Now let's see where the charge will be after some acceleration. So let's say where it is. Now let me draw some field lines and in this case I'll draw only one. So for the charge at its initial position, let's say that the field lines, one field line goes radially outwards like this. Now the region of space outside this sphere has not received the information that the charge has accelerated. So it stays where it is. Whereas the world inside this circle has changed and so are the electric field lines with it. So the electric field line inside the circle it goes along with the charge and it looks looks like this and this will result in the formation of a kink because the electric field line has to join. So the kink looks like this and now this is the electric field line. This is how it goes. Now we can see that this electric field line in the region of the kink is, it is at some angle and we can actually resolve this into components. So it will have a perpendicular component and it will have a radial component of electric field. It is this perpendicular component of electric field in the traveling wave that is part of the electromagnetic wave that moves outward with the speed of light. If you're looking at the wave from here and this whole shell comes over to us, it is only this perpendicular electric field in our line of sight which we can see as moving outwards. Now what could the magnitude of this perpendicular electric field depend upon? We accelerated the charge and that produced a kink in the electric field and upon resolving it into two components, we obtained the perpendicular component and a radial component. Maybe if the kink is even bigger in size then the perpendicular component might even be longer. What could lead to a bigger kink? Maybe let's try and provide some more acceleration to the charge and see what happens. So let me remove the charge at this position. So let's start from the initial position and provide greater acceleration to the charge. So the charge might be somewhere over here now. It has moved further down because it has a greater acceleration. In this case the electric field that goes along with the charge can look like this. Now if we join these electric field lines, we will see that the kink formed in this case is slightly longer, is slightly bigger and upon resolving this kink into components, the electric field in the kink into components, this is how the components could look like and we can see that the perpendicular component, the magnitude of the vertical component is bigger in this case and that happened when we provided the charge with greater acceleration. So if the charge accelerates with a greater magnitude, we get a bigger electric field which propagates again outwards with the speed of light. Now so far we have been accelerating the charge downwards. Let's accelerate it upwards and see what happens. So now we are starting over here at rest and then we will accelerate the charge upwards. At this point the electric field lines and I'll draw only one will look like this and then when we accelerated upwards maybe the charge is over here now. So when the charge is over here the electric field line inside the circle will move along with the charge. So that could that could look somewhat like this. But again we can see that they will be a kink form now because the information of acceleration outside the circle has not reached the electric field. They don't even know. So as a result of which a kink is formed in this direction and now the electric field goes like this from this positive charge go down and then go out. So if we resolve the electric field in this kink region into components, this is how the components will look like. Here we see that the perpendicular component of the electric field is pointing vertically downwards. So when we change the direction of acceleration even the direction of the vertical component of the electric field the perpendicular component that propagates outwards even that direction changes. And if we were to oscillate the charge sinusoidally that is changing the acceleration of the charge sinusoidally which means it increases then it becomes zero then it decreases and increases in the opposite direction. The magnitude of the electric field should change according to that as well and it should change its direction with the direction of acceleration changes. Let's take a look at all of this in an animation. Now if we provide a bump that is accelerating downwards and then quickly upwards, the direction of the electric field vector must change. So let's see how that will look like. There you go. Now if we oscillate the charge sinusoidally we should see kinks that look like sine waves. If we increase the frequency that is if we oscillate it faster we see the sine waves clearer in this case. All right now where does magnetic field come into picture? We can say that the charge is moving up so there can be a magnetic field due to that movement because we know that moving charges produce magnetic fields and if the charge is moving up using the right hand rule pointing a thumb in the direction of the movement of the charge can give us the direction of the magnetic field and that is given by the curl of the fingers. But it turns out that the magnetic field that is produced due to the movement stays alive only for very short distances but for distances far away from the source the magnetic field that is induced is due to the changing electric field and it is the electromagnetic radiation far off from the source that is useful to us that is even detected. The magnetic field that is generated due to the movement dies very quickly close to the charge so if this electric field vector is moving to the right it will it will create a magnetic field that is perpendicular to it and we can figure out the direction of magnetic field or electric field or even the velocity if we know two out of these three vectors. The direction of wave travel is always it's always in the direction of E cross B it's always in the direction of E cross B and this is the direction of this is the direction of wave travel or the direction of velocity so in this case we knew that the wave was moving to the right and the perpendicular component of electric field is vertically down so magnetic field vector had to point away from us into the plane of the screen because if we take the cross product if we take the cross product and use the right hand rule in this case a thumb would be pointing to the right and the curl of the fingers goes from the electric field to the magnetic field when the electric field vector was pointing up even then the wave was moving to the right and in that case the magnetic field would be pointing outwards and we can use the same right hand rule to confirm that so our thumb should be pointing in the direction of the movement of wave and again our fingers they go clockwise they go from E to B E cross B and the direction of E cross B is the direction of wave travel so far off from the source it is the induced electric field that induces a perpendicular component of magnetic field let's see how this looks like in three dimensions so here we have the charge and in this case we are again only accelerating the charge in the downwards direction we are not accelerating it sinusoidally we are only moving it accelerating it downwards we see these electric and magnetic field lines propagate in all the directions at the speed of light so after some time these electric and magnetic field lines might have reached this position they are propagating outwards and after some more time these same lines must have reached at this position notice there is no electromagnetic radiation vertically and we can connect this to what we saw earlier because there is no kink formed in this region so there is no electromagnetic radiation over here now usually in textbooks we see an image somewhat like this a sinusoidal nature of electromagnetic waves this is what we get when we oscillate the charge sinusoidally that is when the charge is accelerated downwards we will see electric field vectors which are pointing in the upward direction and as the acceleration changes so does the magnitude of the electric field vectors and when the acceleration changes its direction so does the direction of the electric field vectors and also the direction of magnetic field changes as the direction of movement of the charge changes but let's try and arrive at this image that you see on the right so for that we will have one charge which will oscillate sinusoidally that is the acceleration will increase and it will decrease then it will again start increasing but in the opposite direction just like a sine wave and let's say that the charge is placed at this position and it is oscillating sinusoidally along the vertical axis now when the charge has an acceleration vertically downwards a maximum acceleration downwards we will get an electric and magnetic field line somewhat like this now when the acceleration changes let's say if it decreases but it is still vertically down this electric and magnetic field vector will keep on propagating it will move forward but you will have a new electric and magnetic field vector which is smaller in length because the magnitude of acceleration has decreased let's say if the acceleration decreased further it is even smaller now you will get a smaller perpendicular electric and magnetic field vector and when the acceleration changes its direction when it is in the opposite direction these vectors they will keep on moving forward with the speed of light so this is where they are now and now you have an electric field in the opposite direction because the direction of acceleration changed now when the magnitude of acceleration increases further in the opposite direction you will get a pair of electric and magnetic field vector again but with greater magnitude in the direction shown and lastly if we keep on doing this you will reach a maximum electric and magnetic field vector just like this now let's try and join the tips of the electric field vectors and the magnetic field vectors so when we do that when we do that for electric field this is how it can look like and for magnetic field it looks like this they are perpendicular to each other even though this is not the full sine curve in the true sense but you can imagine if it continues it will form a sine curve just like this all right so in this video we saw how accelerating charges produce electromagnetic waves that propagate or move in all the directions with the speed of light as a result of the charges acceleration a kink is formed and in that region of kink the perpendicular component of electric field moves outward and it is that changing perpendicular component which induces a perpendicular component of magnetic field which moves outwards along with the electric field and we saw how we can figure out the directions if out of those three vectors that is electric magnetic and the direction of wave travel if out of those three we know two vectors using the right hand curl rule we can figure out the direction of the third one and finally we oscillated the charge sinusoidally and we arrived at an electromagnetic wave which looks like a sine curve or sinusoidal in nature