8.5 Magnetic Domain and Electromagnet from Office of Academic Technologies on Vimeo.

**8.5 Magnetic Domain and Electromagnet**

Earlier we have seen that a circular current loop carrying a current in counterclockwise direction generates magnetic field along its axis in upward direction. We have seen that also if we have a bunch of turns instead of one turn, we defined a quantity called “magnetic dipole moment vector”, which was equal to number of turns times the current flowing through the loop times the area vector, and that is the surface area vector of the region surrounded by the current loop. In other words, the magnetic dipole moment vector was in the same direction with the area vector.

We have seen that for the surfaces, that they are surrounded by current loops, we apply right hand rule in order to determine the direction of the area vector, which we know that it will always be perpendicular to the surface and for such a surface, in other words, a surface surrounded by a current loop, we hold our right hand fingers in the direction of current flow and curl them about the thumb. That direction gives us the associated surface area vector, which is therefore going to be perpendicular to the surface in this direction and will have the magnitude of the area of interest.

Since the magnetic dipole moment vector of this current loop is in the same direction with the area vector, we can easily conclude that the magnetic dipole moment vector associated with a current loop like this is going to be in the same direction with the area vector as well as the magnetic field vector. Therefore it’s going to be something like this.

For a magnetic dipole moment vector, we will have a corresponding magnetic field pointing in the same direction. Now, from this model, if we go into the worlds of atoms, we know that atom consists of a positively nucleus and negatively charged electrons orbiting about the nucleus. An electron is a charged particle which is moving along the nucleus of the atom. In most of the atoms, as the electrons orbit about the nucleus of the atom, the tiny little current loops and their associated magnetic domain vectors, as well as corresponding magnetic fields, are randomly oriented and they simply cancel and we do not end up by having a net magnetic field associated with the motion of those electrons as they orbit about the nucleus or the net magnetic dipole moment vectors.

For some of the materials, electrons orbit about the nuclei of the atoms in a unison way by generating this tiny little current loops and, again, as these materials under normal conditions, these current loops that the orbiting electrons about the nucleus of the atoms, despite the fact that they orbit in a unison way, their associated magnetic domain vectors will be oriented in random directions so we don’t end up with a net magnetic field associated with these magnetic dipole moment vectors.

We can refer these type of regions as the magnetic domains of that material, but we have earlier seen that if we place a current carrying loop in an external magnetic field, that the force generated by the external magnetic field causes a torque and under the influence of this torque, these loops rotate and align along the magnetic field lines. So if we place such a material in an external magnetic field, let’s say pointing in this direction, then these loops rotate and align along the magnetic field lines. When they do, all these tiny little magnetic dipole moment vectors point in the same direction.

Since every magnetic dipole moment vector has an associated magnetic field which is pointing in the same direction, then we end up all these magnetic field vectors adding to one another, therefore generating a net magnetic field of *B*′ in this region.

Well, once this is established, once we’ve removed the external magnetic field, we can end up with two different cases. Those cases are such that these magnetic domains, or the magnetic dipole moment vectors, remain aligned. Therefore, by generating this net magnetic field of the medium, *B*′, when we remove the external magnetic field, we call these types of materials as “permanent magnets”.

On the other hand, for some of the materials, once we remove the external magnetic field, the magnetic dipole moment vectors associated with these tiny little current loops generated from the motion of the electrons as they orbit about the nuclei of the atoms, go back to their random orientations. Therefore the magnetic field associated with each one of these magnetic dipole moment vectors cancel one another when we add them vectorially and we end up again with no net magnetic field in the medium. We call these types of materials as “non-permanent magnets”. A typical example to this case is iron.

In this sense, if we consider a solenoid, something like this, and let’s say we connect the ends of the solenoid to a power supply with a switch *S* over here. Now obviously when we close the switch, we are going to generate *ε* volts of potential difference between the ends of the solenoid and the current will flow from positive to end towards the negative end throughout this solenoid.

Of course this is going to occur once we close the switch and end up with a closed circuit over here. If we place a non-permanent material along the axis of the solenoid, like an iron bar, when we turn the switch on, we will let the current flow through the solenoid. Therefore we are going to generate this external magnetic field, **B**, along the axis of this solenoid, filling the interior region.

This external magnetic field will cause the magnetic dipole moment vectors of the current loops of the non-permanent magnet medium, they will rotate as a result of torque generated by this external magnetic field. They will align, therefore they are going to generate a net magnetic field of *B′* prime throughout the region of this material. Therefore we are going to end up with even a stronger magnetic field generated through a system like this.

One magnetic field is due to the current flowing through the solenoid and the other one, *B*′, is a result of the non-permanent magnet inside of this region getting magnetized due to this external magnetic field. Once we turn the switch off, this current dropped to 0, therefore the external magnetic field goes back to 0. Then the magnetic dipole moment vectors of this non-permanent magnet region will go back to their random orientations. Therefore the associated magnetic fields will cancel one another and we will end up with 0 magnetic field.

Therefore when the switch is on position, we will end up with a total magnetic field which is equal to **B** plus **B**′ prime, a strong magnetic field. When the switch is turned to off position, the external magnetic field will go back to 0, therefore **B**′ prime also will go back to 0. In that case, **B** total will be equal to 0.

This is therefore an interesting system such that we generate a strong magnetic field whenever we turn the switch on and we generate no magnetic field when we turn the switch to off position. Therefore we end up with a magnet. It behaves as a magnet whenever we want it to, and it goes back and becomes a non-magnet again whenever we want to. We call these type of devices as electromagnets.