We are studying magnetism from our high school. We have been introduced to the different types of magnetic materials like Paramagnetic, Diamagnetic, Ferromagnetic materials. In this discussion we only talk about the Diamagnetic materials, we always been taught that diamagnetic material repels the magnetic field. But have you ever questioned why? So, here we will try to dig for the answer to this question. We will see what is happening at the atomic level?
Any charged particle having charge Q which is revolving on a circular loop of radius r produces magnetic field B and has magnetic dipole moment μ associated with this. The time period of this charge revolution is given as :
T = 2πr/v
Here r is the radius of the loop and v is the velocity of the charge moving on a circular loop. Since the current is defined as the flow of charge so the current is also associated with this movement.
I = Q/T
Magnetic moment μ is defined as the property of magnet that tells us about the interaction behavior of any material with the magnet. This Magnetic moment μ can be written as current flow in the area πr2.
μ = I.A
μ = (Q.v/2πr).πr2
μ = (Qmvr/2m)
This factor mvr is known as angular momentum(LZ) which means motion contains in a body in a circular motion. Therefore Magnetic moment μ is equal to:
μ = (Q/2m)LZ
Here are talking about an electron movement which has charge -e. So this Therefore Magnetic moment μ becomes:
μ = (-e/2m)LZ
From this equation, we can easily say that any substance which possesses a magnetic dipole moment must have net nonvanishing angular momentum that is LZ should not be equal to zero.
In Diamagnetic material when we apply the magnetic field through it an induced magnetic field produced in the material and this induced field is in opposite direction to the applied field. Due to this opposite field diamagnetic material repels the magnetic field. To understand this deeply let’s take an example where the magnetic field is applied through the diamagnetic material. Let’s take e1 and e2 two neighboring electrons and the magnetic field is applied inward (k) to them.
When an inward magnetic field applied to diamagnetic material these two electrons e1 and e2 move opposite to each other. From the figure if we take to the nearest point movements of these electrons we can clearly see that e1 is moving toward ei and e2 is moving toward -ei directions, that is both are moving in the opposite direction. Because of this opposite movement to each other, they both have an opposite magnetic dipole moment.
From the above diagram, we can clearly see that e1 will be always pushed inward and e2 will be always pushed outward. Due to this inward and outward motion of these electrons, velocity v1 of e1 increases, acceleration also increases, and the velocity of e2 decreases. Because of this increase in velocity of e1, the time period T of this electron changes as:
T = 2πr/v
We know from our above discussion that: μ = (Qmvr/2m) which means magnetic dipole moment μ is directly proportional to velocity v. From the analysis of above diagram we came to know that v1 is greater than v2, which means magnetic moment μ1 of e1 is greater than the magnetic moment μ2 of e2 from the above proportionality relation. There is another relation that tells us that the magnetic field is directly proportional to magnetization M.
M = χB
Here χ is known as magnetic susceptibility which tells us about that up to how much extent a material is magnetized in a presence of the magnetic field. Since this magnetic moment μ is directly proportional to magnetic field B, then we can clearly say that magnetic moment μ is also directly proportional to magnetization. So we can say that magnetization of e1 is greater than magnetization of e2, which means net magnetization inside the diamagnetic material is in opposite direction to the applied magnetic field and this is the reason why diamagnetic material opposes the applied magnetic field.
Diamagnetism has tremendous technological benefits, Diamagnetic materials are basically expelled the magnetic fields. This means more strong the magnetic field, more strongly the diamagnetic material expels the magnetic field. If the magnetic field is sufficiently strong and the area of a diamagnetic material is also considerably large then this diamagnetic material can easily levitate over the magnetic field.
All materials have a diamagnetic effect present in them but it is not significantly present in paramagnetic and ferromagnetic materials. Superconductors have a significantly large diamagnetic effect present in them and due to this large diamagnetic effect, it expels a complete magnetic field. These materials can easily levitate in the presence of strong permanent magnets. This effect of complete expulsion of the magnetic field is called a Meissner effect. And today’s many technologies is based on this property of magnetic field expulsion. Magnetic levitating trains like Maglev, Hyperloop are the best examples of this effect. These trains are very fast, these are the appropriate examples of our latest technology. This all technology exists today because of our better understanding of physics.