 If you take a bar magnet and break it into two pieces, instead of a separate knot pole and a south pole, we get two smaller bar magnets. Just like if you had a piece of chalk and you break the chalk into two, you'll get two smaller pieces of chalks. Something that really doesn't work with currency notes. Now it turns out that if you keep on breaking these bar magnets into smaller and smaller pieces, you keep on getting newer magnets and this is true right to the level of an atom. Even an atom has a knot pole and a south pole. Now it turns out that there are no magnetic monopoles. There is no magnetic monopole known to exist. You never get a separate knot pole, just a knot pole and just a south pole. The simplest magnetic structure that is known to exist is a magnetic dipole and a bar magnet can be a magnetic dipole. Also a current carrying loop can be a magnetic dipole. Now the goal of this video is to explore Gauss's law of magnetism, which is saying the same thing that magnetic monopoles do not exist but it is using the language of math which is saying a lot but using very less number of words. Alright so let's begin. In our previous videos, we looked at how to calculate electric flux through a closed surface where if we had a closed surface like this, a closed spherical surface and let's say we had a positive charge in the center, we know that the flux that is going through the surface would be given by the closed surface integral of the dot product between the electric field and area which equals the amount of charge enclosed in that surface divided by epsilon naught. Now what if just instead of a single positive charge, a monopole of electric charge, you take an electric dipole inside the Gaussian surface just like this. Now what do you think the electric flux would be? Pause the video and think about it. Alright, I'm sure you'll agree that the electric flux in this case would just be zero because your enclosed charge would come out to be zero. You have a plus Q and you have a minus Q. Even if we look at the field lines, this is how the field lines would look like. You can see that the number of field lines that are leaving the surface is equal to the number of field lines that are entering the surface from the other side. So no matter where you place your electric dipole inside the sphere, your flux will always come out to be a zero. Now let's bring back our magnetic dipole into the picture and this is how it can look like. Again pause the video and think about what would be the magnetic flux in this case. Alright, so the magnetic flux in this case would be zero because there are no monopoles over here. We are taking a magnetic dipole and just like how flux for an electric dipole was zero, similarly the flux for a magnetic dipole is zero. We can even have a look at the field lines and see how geometrically similar they are. We can see that the number of field lines that are leaving the surface equal the number of field lines that are entering the surface from the other side. So now we can think about causes law of magnetism just like causes law of electricity only if we had dipoles and just like it doesn't matter where you place the electric dipole inside the surface, your flux would be zero. Similarly it wouldn't really matter how you place the bar magnet inside the surface. You will always get the magnetic flux to be as zero. Now what if we kept the bar magnet outside the surface, somewhat like this. Let's say this is your surface and your power magnet is just right next to it outside of it. So the magnetic field lines in this case would look like this. Now over here we can still see that the number of magnetic field lines that are entering the surface and that would be two in this case. This is the first one. This is the second one. They equal the number of field lines that are exiting the surface again two. So the net flux is still zero in this case. Let's check if the magnetic flux is zero for a different case. Let's say we move around the magnet and we keep it in this way. Half of the magnet is inside and half of it is outside and the field lines in this case would look like this. Now what do you think the magnetic flux would be? Again pause the video and think about it. Now it turns out that even for this case the magnetic flux is zero. You could think that because half of the magnet is inside and half of it is outside, this would be similar to saying that the positive charge, a positive charge would be inside and a negative charge would be outside. But the key point over here is that magnetic field lines form closed continuous loops. So the field lines even inside the magnet go from south to north pole and this is how they look like. Now if we look closely we can see that the number of field lines that are leaving the surface and that would be five in this case. They equal the number of field lines that are entering the surface from inside the magnet. And we can go on to say that this part right here, the part that is near the surface, we can say that this can be a south pole because after all the field lines are going towards the north pole from this region. Now we can say that because we have a north pole and a south pole inside the magnet this is very similar to having an electric dipole in the same orientation. So an electric dipole would just look like this and we know that whenever there is an electric dipole inside the surface the flux for that would be zero. Similarly if we have a magnetic dipole inside the surface the flux for that will be zero. Alright so in this video we looked at how if you take a piece of bar magnet and you break it into smaller pieces instead of a separate north pole and a south pole all you get are newer pieces of small magnets. And just like how the flux for an electric dipole came out to be zero no matter where you place it inside the Gaussian surface, similarly the flux for a magnetic dipole also came out to be zero and we kept the dipole inside outside and we kept it half inside and half outside. In all the cases it came out to be zero. Now if we compare Gauss's law for magnetism with Gauss's law for electricity we can see a noticeable difference. We can see that there is something on the right hand side for Gauss's law of electricity and that is because there is a monopole of electric charge. You can see a single positive charge and a single negative charge and but we can never see a single north pole and a single south pole. So therefore you see a zero over here. Now it turns out that scientists have been searching for a magnetic monopole for almost 90 years now and they have been to the north pole, they have been to deep under waters but they haven't been able to find one. And imagine if they do find one firstly the right hand side of this equation will change. This equation the Gauss's law for magnetism will look very similar to Gauss's law for electricity. You will have something something like a magnetic charge over here and the entire set of Maxwell equations will become beautifully symmetric. We will talk about Maxwell equations in depth in upcoming videos.