We’re all familiar with magnets. If you consider a bar magnet and place a piece of paper on it or a piece of glass plate and then sprinkle some iron particles, we will see that these particles will align along some specific lines. And if you consider several of these lines, they will look like something like this.
If you look at the configuration of these lines, we will see that they never intersect with one another and they always close upon themselves by forming closed loops. We call these lines as magnetic field lines.
Magnetic field lines have exactly similar types of properties as in the case of electric field lines. In other words, the number density of these lines, or the number of lines passing through a unit’s surface is directly proportional to the strength of the field in that region.
Well, again, from magnets, we’re familiar that if we consider two magnets, two bar magnets, let’s say, and place them nearby, something like this, we see that depending upon the faces or the ends that are facing each other, these two magnets either repel or attract one another, and if we do the similar type of observation by placing a glass plate or a piece of paper over these magnets and pour some iron filings, we will see that for the case of attractive force, whenever they attract each other, the lines align such that they join together to form a line geometry something like this.
And in the other case, if we just rotate 1 of the magnets 180 degrees, we will see that, in this case, the magnets repel one another. And for this case, when we place a piece of paper and pour some iron filings on it, we see that the field lines associated with each one of these magnets align something like this.
So, in the previous case, these two magnets exert a force to one another which is an attractive nature. In other words, if we call this one, for example, as our magnet 1, and this one as our magnet 2, the magnet 1 attracts magnet 2 towards itself. So let’s call this force as F21, the force on magnet 2 due to the magnet 1. Similarly magnet 2 attracts magnet 1 with a force of F12, which is force on magnet 1 due to magnet 2.
So, F21 is the force on magnet 1 due to magnet 2, and similarly, F12 is the force on magnet 2 due to magnet 1. And, of course, these forces are equal in magnitude, and also we can say that they’re actually the result of Newton’s Third Law, action-reaction forces. If magnet 1 is attracting magnet 2, then the magnet 2 reacts to that by attracting magnet 1, for this first case. And in the second case, we see that the magnet 1 repels magnet 2 with a force of F21, and similarly magnet 2 repels magnet 1 with a force of F12.
It is because of this attractive and repulsive nature of the forces that the two magnets exert one another. Physicists look for a link between the magnetic forces and the electrical forces, as we recall, which are, also, depending upon the nature of the charges, can be either attractive or repulsive in nature.
And in the electrical interactions case, in order to separate the nature, these two different types of nature of the charge from one another, physicists introduced the concept of positive and negative charge, and here, in a similar way, in order to, again, differ the attractive and repulsive nature of these magnetic forces put on one another, for a given pair of magnets, physicists introduced the concept of north and south pole.
First of all, the regions in which are, we can also see that the end points of these magnets, bar magnets, that we have the maximum number of field lines density, in other words, the number of lines passing through a unit area is the maximum, and in order to differ these regions from the other regions physicists call these points as north, points as poles, and, again, to be able to explain the attractive and repulsive nature of these forces, they introduced the concept of north pole and the south pole. So, they simply called one end as the north pole and the other end as the south pole of the magnet.
Obviously, the field lines have some directional properties, and conventionally, physicists assigned a direction to these field lines such that they originate from the north pole and enter into the south pole for a given magnet. And, of course, inside of the magnet they go from south to north.
So, from this point of view then, we can easily see that if this is the north pole of the magnet and if this is the south pole of this magnet 1, therefore, the field lines are going to be emerging from the north. So this other end should be the south pole in order for them to enter into the pole, and then they go through the magnet 2, and then they will emerge from the north pole of this magnet 2 and eventually will go and enter into the south pole of the first magnet.
On the other hand, I’m going to look at the second case. Again, if we call this one as the north pole of magnet 1 and the lines are emerging from the north and they go and enter into the south, so it’s in the second case we just rotate the second magnet 180 degrees and therefore this end becomes the north pole of the magnet 2, and thereto, the lines emerge from the north and enter into the south pole.
These configurations, therefore, tell us that, or shows us that for a given two magnets if they’re on like poles facing to one another, or nearby to one another, then the nature of the force that they exert to each other is an attractive one. On the other hand if their like poles are nearby or facing to each other, then the nature of the force, the magnetic force that they exert to each other is a repulsive one.
So, that enables us to write down, let’s say, the first property of the magnetic poles by saying that like poles repel, unlike poles attract each other. And this is exactly similar to the electric charges. In that case we have seen that the like charges repel one another. On the other hand, unlike charges attract one another.
Again, as I mentioned earlier, it is because of this similarity physicists look for a link between electricity and magnetism. But for a long time they couldn’t find the link. Therefore, these two branches of physics developed as two separate branches of physics as electricity and magnetism.
But later on, in 1819, a link has been discovered by Danish scientists Hans Christian Orsted as a result of an accident discovery, which we will talk about that in a moment.
But before we go into that part, here now, since we introduced the concept of magnetic field lines let’s now introduce the concept of magnetic fields, which we’re going to denote this quantity by B. Since the field lines naturally have an associative direction, then the magnetic field also has a unique direction. And if you recall the field lines properties from electric field lines, we have seen that the electric field was tangent to the field line passing through the point of interest.
So we have exactly the same situation over here, and therefore, if we just go ahead and note to magnetic field, B field line properties, the first one is that the number of field lines, or I should say B field lines, magnetic field lines, passing through a unit’s surface is directly proportional to the strength of the magnetic field B in that region.
The second property is such that, this is associated with the direction of the field lines, and let’s make a note of that, magnetic field lines emerge from the north pole and enter into the south pole of a given magnet.
And the third property is no two field lines intersect with one another. It means that there will be only a one single unit field line, magnetic field line, passing through a given point. We cannot have two field lines intersecting at that point.
So, up to here, these are the similar types of features, also, the electric field lines shared. The fourth feature is a unique feature for the magnetic field lines and that is magnetic field lines always close upon themselves.
Now, if you recall the electric field lines, we have seen that for an isolated positive point charge, the electric field lines emerge from the charge and go radially outward direction to infinity. And for an isolated negative point charge, for example, an electron, then the field lines come from infinity in radially inward directions and emerge into the charge. So, in that case, because I have ended up with open field lines that are expanding in radial direction to infinity or coming from infinity. Whereas in the case of magnetic field lines we see that no matter what, they always close upon themselves. I will explain this, why this is happening in a moment.
And the fifth property is associated with the direction of the magnetic field, and it is, again, similar to the case of electric field, B field is tangent to the magnetic field line passing through the point of interest. Therefore, if we go back to our diagram over here, the magnetic field, strength will be proportional to the number of field lines passing through a unit’s surface, and we can see that since we have the maximum field lines passing through a unit’s surface existing at the poles of the magnet, we have the maximum strength at the poles. At these points the magnetic field is tangent to the field line passing through a point at this location. So if we’re interested at this point, for example, here, then the magnetic field line will be tangent to this line. Therefore something like this, and pointing in this direction.
And if we’re interested with a point right here, there, it’s going to be tangent to the field line passing through that point. Therefore it will be pointing in this direction. And here, with a point like this, it is going to be pointing in this direction. And as you can see, since the length of the vector is proportional to its magnitude we will have a stronger magnetic field at the poles or near the poles relative to the points which are away from the poles.
Alright. Now in terms of having close field lines all the time, let’s consider, again, a simple experiment. Let’s assume that we have a bar magnet with the north pole over here and the south pole over here. If we break this bar magnet from the middle and consider this half, we will see that that too will have north and south poles. And if we, again, break that magnet from the middle and consider one of the halves, we will see that that piece also will have north and south pole together.
If we continue this breaking process to the smallest pieces that we can break this magnet into, we will see that that piece will too have north and south poles together. And since we have seen that field lines emerge from the north pole and enter into the south pole, like this, and as long as north and south is together, therefore they will always close upon themselves by forming these closed loops.
So no matter what we do, then, we cannot have a case that the north pole by itself or south pole by itself. That brings us another very important feature of the magnetic field lines, and that is directly linked to the property four which says the magnetic field lines always close upon themselves. Let me add a little, one more part over here, saying that forming closed loops. So, magnetic field lines always close upon themselves forming closed loops.
This property four is directly linked to property six, which states that there can not be any magnetic monopoles. Magnetic poles are always in the form of dipoles. In other words, that is north and south pole together, and it is because of this reason magnetic field lines always close upon themselves because the field lines emerging from the north enters into the south and goes from south to north inside of the magnet, forming these closed magnetic field lines.
One can, of course, ask a question of what is the biggest or largest magnet on the Earth question, and the answer is the Earth itself. If we consider the Earth, we see that it has an associated magnetic field. If this represents the geographic north pole and the other end is, of course, the geographic south pole, so GNP is the geographic north pole, and GSP represents the geographic south pole, it turns out to be that the magnetic south pole is nearer to the geographic north and the magnetic north pole is naturally near to the geographic south pole.
So magnetic south pole is the MSP, and magnetic north pole is the MNP. Therefore the magnetic field line geometry of the Earth is such that the field lines are emerging from the magnetic north and entering into the magnetic south, therefore generating field lines of this geometry.
Now, we know that a compass is nothing but a small magnet. A compass needle is a small magnet free to rotate about an axis, and if we represent the compass needle with this symbol over here with being this one as the north pole and the south pole of the magnet, and therefore whenever we hold a compass near the surface of the earth, since these field lines are emerging from the magnetic north and entering into the magnetic south, the north pole of the compass needle is going to be attracted by the magnetic south pole, which is nearby to the geographic north pole, and therefore that the needle will take a position tangent to these field lines.
Therefore, it will point a direction which will be nearer to the geographic north pole, and as a result of this, one can determine the direction on the surface of the earth, or near the surface of the earth, because the compass needle will align along the magnetic field line of the earth, passing through that specific point.