What is the relationship between polarization and electric susceptibility of dielectric material?
2 Answers
The relationship between **polarization (P)** and **electric susceptibility (χₑ)** in a dielectric material is central to understanding how dielectrics respond to an external electric field. Let’s break it down in a detailed manner so that it is clear to everyone.
### 1. **Polarization (P)**
Polarization in a dielectric material refers to the alignment or redistribution of electric dipoles within the material when subjected to an external electric field. This dipole alignment happens because dielectric materials consist of molecules that either have permanent dipoles or develop dipoles in response to an electric field.
When an external electric field (\( \mathbf{E} \)) is applied, these dipoles align in such a way that their positive and negative charges are separated, creating a net electric dipole moment per unit volume in the material. This dipole moment per unit volume is called **polarization (P)**, and it represents how much the material becomes polarized in response to the field. In a linear dielectric material, \( P \) is proportional to the applied electric field.
The **polarization (P)** is mathematically expressed as:
\[
\mathbf{P} = \varepsilon_0 \chi_e \mathbf{E}
\]
Where:
- \( \mathbf{P} \) = Polarization (vector quantity, dipole moment per unit volume),
- \( \varepsilon_0 \) = Permittivity of free space (a constant value in a vacuum),
- \( \chi_e \) = Electric susceptibility of the material (a measure of how easily the material becomes polarized),
- \( \mathbf{E} \) = Applied electric field (vector quantity).
### 2. **Electric Susceptibility (χₑ)**
Electric susceptibility (\( \chi_e \)) is a dimensionless quantity that describes how easily a material becomes polarized when subjected to an external electric field. It characterizes the degree of polarization a material experiences relative to the strength of the applied field.
- If \( \chi_e \) is high, the material polarizes more easily, which means it develops a strong dipole moment for a given electric field.
- If \( \chi_e \) is low, the material polarizes less readily.
### 3. **Relationship Between Polarization and Electric Susceptibility**
The electric susceptibility (\( \chi_e \)) directly relates the polarization (\( \mathbf{P} \)) of the dielectric material to the applied electric field (\( \mathbf{E} \)) through the equation:
\[
\mathbf{P} = \varepsilon_0 \chi_e \mathbf{E}
\]
This equation highlights a linear relationship between the two in a simple dielectric material:
- **Polarization is proportional to the applied electric field**. The stronger the electric field, the greater the alignment of the dipoles within the dielectric, and thus, the greater the polarization.
- **The proportionality constant is the electric susceptibility** \( \chi_e \). It quantifies how much the material will polarize for a given electric field strength. If \( \chi_e \) is large, even a small electric field will cause significant polarization.
### 4. **Physical Interpretation**
- When an electric field is applied to a dielectric material, the dipoles within the material align with the field. This alignment creates a polarization field, which effectively reduces the internal electric field within the material.
- **Electric susceptibility** determines how much the internal dipoles of the dielectric material align with the applied field. A high susceptibility means the material becomes highly polarized, reducing the external electric field inside the material significantly.
### 5. **Relation to Permittivity**
The electric susceptibility \( \chi_e \) is also related to the **relative permittivity** \( \varepsilon_r \) (also called the dielectric constant) of the material:
\[
\varepsilon_r = 1 + \chi_e
\]
Where:
- \( \varepsilon_r \) is the relative permittivity of the material, which describes how much the material can reduce the electric field within it compared to free space.
The relative permittivity tells you how much the material can "permit" the electric field to pass through it, and it directly depends on the electric susceptibility.
### 6. **Summary**
- **Polarization (P)** represents the dipole moment per unit volume within a dielectric material caused by an applied electric field.
- **Electric susceptibility (χₑ)** measures how easily a dielectric material becomes polarized in response to the electric field.
- The relationship is given by \( \mathbf{P} = \varepsilon_0 \chi_e \mathbf{E} \), meaning polarization is proportional to the electric field, and the proportionality constant is \( \varepsilon_0 \chi_e \).
- The higher the electric susceptibility, the more polarizable the material, and the higher the resulting polarization for a given electric field.
Thus, the electric susceptibility \( \chi_e \) is a key factor in determining how much polarization occurs in a dielectric when exposed to an electric field.
### 1. **Polarization (P)**
Polarization in a dielectric material refers to the alignment or redistribution of electric dipoles within the material when subjected to an external electric field. This dipole alignment happens because dielectric materials consist of molecules that either have permanent dipoles or develop dipoles in response to an electric field.
When an external electric field (\( \mathbf{E} \)) is applied, these dipoles align in such a way that their positive and negative charges are separated, creating a net electric dipole moment per unit volume in the material. This dipole moment per unit volume is called **polarization (P)**, and it represents how much the material becomes polarized in response to the field. In a linear dielectric material, \( P \) is proportional to the applied electric field.
The **polarization (P)** is mathematically expressed as:
\[
\mathbf{P} = \varepsilon_0 \chi_e \mathbf{E}
\]
Where:
- \( \mathbf{P} \) = Polarization (vector quantity, dipole moment per unit volume),
- \( \varepsilon_0 \) = Permittivity of free space (a constant value in a vacuum),
- \( \chi_e \) = Electric susceptibility of the material (a measure of how easily the material becomes polarized),
- \( \mathbf{E} \) = Applied electric field (vector quantity).
### 2. **Electric Susceptibility (χₑ)**
Electric susceptibility (\( \chi_e \)) is a dimensionless quantity that describes how easily a material becomes polarized when subjected to an external electric field. It characterizes the degree of polarization a material experiences relative to the strength of the applied field.
- If \( \chi_e \) is high, the material polarizes more easily, which means it develops a strong dipole moment for a given electric field.
- If \( \chi_e \) is low, the material polarizes less readily.
### 3. **Relationship Between Polarization and Electric Susceptibility**
The electric susceptibility (\( \chi_e \)) directly relates the polarization (\( \mathbf{P} \)) of the dielectric material to the applied electric field (\( \mathbf{E} \)) through the equation:
\[
\mathbf{P} = \varepsilon_0 \chi_e \mathbf{E}
\]
This equation highlights a linear relationship between the two in a simple dielectric material:
- **Polarization is proportional to the applied electric field**. The stronger the electric field, the greater the alignment of the dipoles within the dielectric, and thus, the greater the polarization.
- **The proportionality constant is the electric susceptibility** \( \chi_e \). It quantifies how much the material will polarize for a given electric field strength. If \( \chi_e \) is large, even a small electric field will cause significant polarization.
### 4. **Physical Interpretation**
- When an electric field is applied to a dielectric material, the dipoles within the material align with the field. This alignment creates a polarization field, which effectively reduces the internal electric field within the material.
- **Electric susceptibility** determines how much the internal dipoles of the dielectric material align with the applied field. A high susceptibility means the material becomes highly polarized, reducing the external electric field inside the material significantly.
### 5. **Relation to Permittivity**
The electric susceptibility \( \chi_e \) is also related to the **relative permittivity** \( \varepsilon_r \) (also called the dielectric constant) of the material:
\[
\varepsilon_r = 1 + \chi_e
\]
Where:
- \( \varepsilon_r \) is the relative permittivity of the material, which describes how much the material can reduce the electric field within it compared to free space.
The relative permittivity tells you how much the material can "permit" the electric field to pass through it, and it directly depends on the electric susceptibility.
### 6. **Summary**
- **Polarization (P)** represents the dipole moment per unit volume within a dielectric material caused by an applied electric field.
- **Electric susceptibility (χₑ)** measures how easily a dielectric material becomes polarized in response to the electric field.
- The relationship is given by \( \mathbf{P} = \varepsilon_0 \chi_e \mathbf{E} \), meaning polarization is proportional to the electric field, and the proportionality constant is \( \varepsilon_0 \chi_e \).
- The higher the electric susceptibility, the more polarizable the material, and the higher the resulting polarization for a given electric field.
Thus, the electric susceptibility \( \chi_e \) is a key factor in determining how much polarization occurs in a dielectric when exposed to an electric field.
The relationship between polarization and electric susceptibility in dielectric materials is fundamental to understanding how these materials respond to electric fields. Let's break this down into clear concepts:
### **1. Polarization**
**Polarization** refers to the alignment of electric dipoles within a dielectric material when it is subjected to an external electric field. In a dielectric material, molecules or atoms have intrinsic electric dipole moments. When an electric field is applied, these dipoles tend to align with the field, leading to a net polarization of the material.
Mathematically, the polarization \( \mathbf{P} \) of a dielectric material is the dipole moment per unit volume:
\[ \mathbf{P} = \frac{\text{Dipole Moment}}{\text{Volume}} \]
### **2. Electric Susceptibility**
**Electric susceptibility** (denoted by \( \chi_e \)) is a measure of how easily a material can be polarized by an external electric field. It quantifies the degree to which a material becomes polarized in response to an electric field. Susceptibility is a dimensionless quantity and is defined as:
\[ \chi_e = \frac{\mathbf{P}}{\epsilon_0 \mathbf{E}} \]
where \( \mathbf{E} \) is the external electric field, and \( \epsilon_0 \) is the permittivity of free space.
### **Relationship Between Polarization and Susceptibility**
The relationship between polarization \( \mathbf{P} \) and electric susceptibility \( \chi_e \) can be described by:
\[ \mathbf{P} = \epsilon_0 \chi_e \mathbf{E} \]
Here’s a step-by-step breakdown:
1. **Applied Electric Field and Polarization**: When an electric field \( \mathbf{E} \) is applied to a dielectric material, it causes a polarization \( \mathbf{P} \) in the material.
2. **Proportional Relationship**: The polarization \( \mathbf{P} \) is directly proportional to the applied electric field \( \mathbf{E} \), with the proportionality constant being \( \epsilon_0 \chi_e \), where \( \epsilon_0 \) is the permittivity of free space. This constant reflects the material’s susceptibility to polarization.
3. **Electric Susceptibility**: Electric susceptibility \( \chi_e \) essentially describes how much polarization \( \mathbf{P} \) is induced per unit electric field \( \mathbf{E} \). A higher susceptibility means the material is more easily polarized.
### **Physical Interpretation**
- **High Susceptibility**: Materials with high susceptibility (like many ferroelectrics) will exhibit a large polarization for a given electric field. These materials can have significant responses even with relatively weak electric fields.
- **Low Susceptibility**: Materials with low susceptibility (such as some insulating materials) will show a smaller polarization for the same electric field.
### **Summary**
In essence, electric susceptibility \( \chi_e \) provides a measure of how strongly a dielectric material will polarize in response to an electric field. Polarization \( \mathbf{P} \) is the actual dipole moment per unit volume induced in the material by the electric field. The relationship \( \mathbf{P} = \epsilon_0 \chi_e \mathbf{E} \) succinctly connects these two concepts, linking the material's intrinsic properties (through susceptibility) to its response to an applied electric field (through polarization).
### **1. Polarization**
**Polarization** refers to the alignment of electric dipoles within a dielectric material when it is subjected to an external electric field. In a dielectric material, molecules or atoms have intrinsic electric dipole moments. When an electric field is applied, these dipoles tend to align with the field, leading to a net polarization of the material.
Mathematically, the polarization \( \mathbf{P} \) of a dielectric material is the dipole moment per unit volume:
\[ \mathbf{P} = \frac{\text{Dipole Moment}}{\text{Volume}} \]
### **2. Electric Susceptibility**
**Electric susceptibility** (denoted by \( \chi_e \)) is a measure of how easily a material can be polarized by an external electric field. It quantifies the degree to which a material becomes polarized in response to an electric field. Susceptibility is a dimensionless quantity and is defined as:
\[ \chi_e = \frac{\mathbf{P}}{\epsilon_0 \mathbf{E}} \]
where \( \mathbf{E} \) is the external electric field, and \( \epsilon_0 \) is the permittivity of free space.
### **Relationship Between Polarization and Susceptibility**
The relationship between polarization \( \mathbf{P} \) and electric susceptibility \( \chi_e \) can be described by:
\[ \mathbf{P} = \epsilon_0 \chi_e \mathbf{E} \]
Here’s a step-by-step breakdown:
1. **Applied Electric Field and Polarization**: When an electric field \( \mathbf{E} \) is applied to a dielectric material, it causes a polarization \( \mathbf{P} \) in the material.
2. **Proportional Relationship**: The polarization \( \mathbf{P} \) is directly proportional to the applied electric field \( \mathbf{E} \), with the proportionality constant being \( \epsilon_0 \chi_e \), where \( \epsilon_0 \) is the permittivity of free space. This constant reflects the material’s susceptibility to polarization.
3. **Electric Susceptibility**: Electric susceptibility \( \chi_e \) essentially describes how much polarization \( \mathbf{P} \) is induced per unit electric field \( \mathbf{E} \). A higher susceptibility means the material is more easily polarized.
### **Physical Interpretation**
- **High Susceptibility**: Materials with high susceptibility (like many ferroelectrics) will exhibit a large polarization for a given electric field. These materials can have significant responses even with relatively weak electric fields.
- **Low Susceptibility**: Materials with low susceptibility (such as some insulating materials) will show a smaller polarization for the same electric field.
### **Summary**
In essence, electric susceptibility \( \chi_e \) provides a measure of how strongly a dielectric material will polarize in response to an electric field. Polarization \( \mathbf{P} \) is the actual dipole moment per unit volume induced in the material by the electric field. The relationship \( \mathbf{P} = \epsilon_0 \chi_e \mathbf{E} \) succinctly connects these two concepts, linking the material's intrinsic properties (through susceptibility) to its response to an applied electric field (through polarization).