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Definition of Magnetisation
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Today we will discuss magnetisation. Let's start by defining it. Magnetisation, denoted as M, represents the net magnetic moment per unit volume in a material. Does anyone know how we express it mathematically?
Is it M equals magnetic moment divided by volume?
That's right! It's defined as M = m/V, where m is the net magnetic moment and V is the volume. Can anyone tell me what units we would use for magnetisation?
I think it's A/m, isn't it?
Exactly! Magnetisation is measured in A/m. Remember, a positive magnetic moment indicates the direction of flow of magnetic fields in the substance. As we move forward, remember this definition because itβs essential for our understanding of magnetic fields.
Introduction to Magnetic Intensity
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Now, let's shift to magnetic intensity, denoted as H. Who can explain how it is mathematically represented?
H is given by B/ΞΌβ - M, where B is the magnetic field, right?
Correct! H is defined as H = B/ΞΌβ - M. It essentially helps us understand the influence of external currents on the magnetic field. What's interesting is that we relate this back to magnetisation. Can anyone summarize why these concepts are related?
Since H includes the material's response to the external field, it shows us how M affects the overall magnetic field.
Exactly! The two concepts are interdependent. Our next step will be looking at their implications on various materials.
Understanding the Magnetic Field Equation
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Now that we've defined magnetic intensity and magnetisation, let's look at how they come together in magnetic fields. The total magnetic field B can be expressed as B = ΞΌβ(H + M). Can anyone explain what this means?
It shows that the total magnetic field is a combination of external factors and the material's response!
Exactly! This equation helps us predict the magnetic behavior in different materials, especially when we consider their susceptibility. What can you tell me about the relationship between susceptibility and magnetisation?
Susceptibility describes how a material responds to a magnetic field. It's often represented as Ο.
You're spot on! And for classification purposes, this impacts whether materials are diamagnetic, paramagnetic, or ferromagnetic.
Exploring Magnetic Material Classification
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As we classify magnetic materials, we find three categories: diamagnetic, paramagnetic, and ferromagnetic. Let's discuss diamagnetic. What do you know about it?
Diamagnetic materials are weakly repelled by a magnetic field.
Correct! And what about paramagnetic materials?
Paramagnetic materials are weakly attracted to magnetic fields.
Exactly, and they have positive susceptibility. Finally, what can you tell us about ferromagnetic materials?
They are strongly attracted to magnetic fields and retain their magnetisation.
Great summary! Understanding these classifications is essential in applications like technological devices and materials science.
Introduction & Overview
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Quick Overview
Standard
Magnetisation is defined as the net magnetic moment per unit volume in a material, while magnetic intensity is related to the magnetic field produced by external currents. This section highlights how these concepts interact and contribute to understanding various magnetic properties of materials.
Detailed
Detailed Summary of Magnetisation and Magnetic Intensity
In this section, two key concepts are defined: magnetisation (M) and magnetic intensity (H). Magnetisation, expressed as M = net magnetic moment / volume, quantifies how a material responds to an external magnetic field by reflecting its net magnetic moment per unit volume. The units for magnetisation are A/m.
Magnetic intensity, on the other hand, is defined as an auxiliary field that helps describe the effect of external currents on magnetic fields. It is represented as H =
B/ΞΌβ - M, where B is the magnetic field, and ΞΌβ is the permeability of free space. This reveals that magnetic field B can be understood as resulting from both the external magnetic intensity H and the material's response M.
The relationship can be expressed as B = ΞΌβ(H + M), which allows for further analysis of different materialsβdiamagnetic, paramagnetic, and ferromagneticβby examining how their magnetic properties respond to magnetisation and magnetic intensity. The significance of understanding these concepts lies in their application to classifying and quantifying the magnetic behavior of various substances used in technological innovations.
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Definition of Magnetisation
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In the present section, we define and explain certain terms which will help us to carry out this exercise. We have seen that a circulating electron in an atom has a magnetic moment. In a bulk material, these moments add up vectorially and they can give a net magnetic moment which is non-zero. We define magnetisation M of a sample to be equal to its net magnetic moment per unit volume:
M = net / V
M is a vector with dimensions Lβ1 A and is measured in a units of A mβ1.
Detailed Explanation
Magnetisation is the measure of the magnetic moment in a material. Essentially, it tells us how much of a magnetic moment is present in a given volume of material.
- Each individual electron in an atom behaves like a tiny magnet due to its spin and orbit around the nucleus.
- When many atoms are put together, their individual magnetic moments can add together. This can lead to a situation where the material as a whole has a net magnetic moment.
- The formula for magnetisation, M = net / V, tells us how strong this magnetic effect is in a specific volume (V) of material.
Examples & Analogies
Think of magnetisation like the strength of an army in a region. Every soldier (electron) contributes to the overall might of the army (bulk material). If all the soldiers align their efforts (magnetic moments), the army becomes significantly stronger (net magnetic moment).
Magnetic Field Inside a Solenoid
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Consider a long solenoid of n turns per unit length and carrying a current I. The magnetic field in the interior of the solenoid was shown to be given by
B = Β΅_0 nI
If the interior of the solenoid is filled with a material with non-zero magnetisation, the field inside the solenoid will be greater than B_0. The net B field in the interior of the solenoid may be expressed as
B = B_0 + B_m
where B_m is the field contributed by the material core. It turns out that this additional field B_m is proportional to the magnetisation M of the material and is expressed as
B_m = Β΅_0 M.
Detailed Explanation
When we pass electric current through a solenoid, it creates a magnetic field inside due to the turns of wire that are tightly wound. This can be described mathematically.
- The magnetic field B in a solenoid filled with air or vacuum is given by the equation B = Β΅_0 nI, where n is the number of turns per unit length and I is the current.
- However, if we fill the solenoid with a magnetic material that has magnetisation (M), the magnetic field increases because the material contributes additional magnetic field B_m, which is proportional to its own magnetisation.
Examples & Analogies
Imagine a water hose (the solenoid) flowing water (the current). If you put a sponge (the magnetic material) into the hose, it absorbs even more water, increasing the overall flow. The sponge represents how materials can enhance the magnetic field in a solenoid.
Introduction of Magnetic Intensity
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It is convenient to introduce another vector field H, called the magnetic intensity, which is defined by
H = B / Β΅_0 - M.
Thus, the total magnetic field B is written as
B = Β΅_0 (H + M).
Detailed Explanation
Magnetic intensity (H) provides a way to describe the magnetic environment in a material that separates the effects of external fields from internal material properties.
- The equation H = B / Β΅_0 - M helps to determine how the magnetic field interacts with the material's own properties.
- This is essential because B includes contributions from both the external applied field and the material's magnetisation (M).
Examples & Analogies
Think of magnetic intensity as the total loudness of a concert (B), which includes the background noise (external field) and the music of the band (magnetisation). Magnetic intensity (H) helps you understand how much of the loudness is due to just the band alone, separate from the background noise.
Understanding Magnetic Susceptibility
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The latter quantity can be influenced by external factors. This influence is mathematically expressed as M = Ο H, where Ο, a dimensionless quantity, is appropriately called the magnetic susceptibility. It is a measure of how a magnetic material responds to an external field.
Detailed Explanation
Magnetic susceptibility (Ο) indicates how easily a material can be magnetised in an external magnetic field.
- A larger positive value of Ο means the material can be easily magnetised (paramagnetic materials), while a negative value (diamagnetic materials) means it resists magnetisation.
- This relationship helps us understand the response of different materials when they are subjected to magnetic fields.
Examples & Analogies
Consider magnetic susceptibility like a sponge's ability to soak up water. Some materials (sponges) absorb water (get magnetised) easily due to high susceptibility, while others (like a leaf) hardly do, representing low or negative susceptibility.
The Relationship between B, H, and M
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From Eqs. (5.12) and (5.13) we obtain,
B = ΞΌ_0 (1 + Ο) H
where ΞΌ = 1 + Ο is a dimensionless quantity called the relative magnetic permeability of the substance.
Detailed Explanation
The relationship between B, H, and M helps us to further elaborate on how to describe magnetic fields within various materials, especially in terms of how these materials respond to external changes in the magnetic field.
- Understanding this relationship allows us to predict how materials will behave in different situations and fields.
Examples & Analogies
You can compare this relationship to understanding how a car's engine responds to the accelerator. How much power you get (B) depends on how much you push the gas pedal (H) and the efficiency of your engine (M).
Definitions & Key Concepts
Learn essential terms and foundational ideas that form the basis of the topic.
Key Concepts
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Magnetisation and its Definition: The net magnetic moment per unit volume in a material, signifying how materials respond to magnetic fields.
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Magnetic Intensity Concept: A vital vector quantity that aids in describing interactions between magnetic fields and materials.
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Magnetic Susceptibility: Indicates the responsiveness of a material's magnetisation to an applied magnetic field.
Examples & Real-Life Applications
See how the concepts apply in real-world scenarios to understand their practical implications.
Examples
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Example of magnetisation: A bar magnet retains a net magnetic moment, indicating its magnetisation when placed in a magnetic field.
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Example of magnetic intensity: In a solenoid, the intensity varies based on its current and the core material, affecting the magnetic field generated.
Memory Aids
Use mnemonics, acronyms, or visual cues to help remember key information more easily.
π΅ Rhymes Time
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Magnetisation's net we see, moments per volume, as clear as can be!
π Fascinating Stories
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Imagine a field with strong poles. Each material shows a role, some attracted, some pushed away; that's how they play!
π§ Other Memory Gems
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To remember types of materials: 'P-F-D' for Paramagnetic, Ferromagnetic, and Diamagnetic.
π― Super Acronyms
Use 'MHS' to remember
- M: for Magnetisation
- H: for Magnetic Intensity
- S: for Susceptibility.
Flash Cards
Review key concepts with flashcards.
Glossary of Terms
Review the Definitions for terms.
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Term: Magnetisation
Definition:
The net magnetic moment per unit volume in a material, usually denoted as M.
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Term: Magnetic Intensity
Definition:
The vector field that describes the contribution to the magnetic field from electric currents, denoted as H.
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Term: Magnetic Moment
Definition:
A vector quantity that represents the strength and direction of a magnetic source.
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Term: Magnetic Susceptibility
Definition:
A dimensionless quantity that indicates the degree of magnetisation of a material in response to an applied magnetic field.
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Term: Permeability
Definition:
A measure of how easily a material can support the formation of a magnetic field within itself.