Why electric field inside a dielectric decreases due to polarisation?
2 Answers
To understand why the electric field inside a dielectric material decreases due to polarization, let's break down the concepts step by step:
### 1. **Basic Concepts**
**Dielectric Material:** A dielectric is an insulating material that does not conduct electricity but can support an electrostatic field. When placed in an electric field, dielectrics exhibit polarization.
**Electric Field (\(\vec{E}\)):** This is the force per unit charge experienced by a charged particle in space due to other charges or fields.
**Polarization (\(\vec{P}\)):** Polarization refers to the alignment of electric dipoles in the dielectric material. When a dielectric is placed in an electric field, the positive and negative charges in the dielectric material slightly shift, creating an induced electric dipole moment per unit volume.
### 2. **Effect of Polarization on the Electric Field**
When a dielectric material is placed in an external electric field (\(\vec{E}_{\text{ext}}\)), it becomes polarized. Here's how this affects the electric field inside the dielectric:
#### a. **Induced Dipoles and Internal Field**
- **Polarization Charge:** The shifting of charges creates bound surface charges on the surface of the dielectric, which results in an internal electric field (\(\vec{E}_{\text{int}}\)) opposing the external field. This internal field is due to the dipole moments induced by the external electric field.
- **Opposing Field:** The induced dipole moments in the dielectric create an electric field that acts in the opposite direction to the external electric field. This is because the negative ends of the dipoles are oriented towards the positive side of the external field, and vice versa.
#### b. **Electric Displacement Field (\(\vec{D}\))**
The electric displacement field \(\vec{D}\) accounts for the effects of polarization:
\[ \vec{D} = \epsilon_0 \vec{E} + \vec{P} \]
where:
- \(\epsilon_0\) is the permittivity of free space,
- \(\vec{E}\) is the electric field inside the dielectric,
- \(\vec{P}\) is the polarization vector.
For a given external electric field \(\vec{E}_{\text{ext}}\), the relationship between the electric displacement field \(\vec{D}\) and \(\vec{E}_{\text{ext}}\) is:
\[ \vec{D} = \epsilon \vec{E}_{\text{ext}} \]
where \(\epsilon\) is the permittivity of the dielectric, which is higher than \(\epsilon_0\).
#### c. **Reduced Internal Electric Field**
The internal electric field \(\vec{E}\) within the dielectric material is related to the external field by:
\[ \vec{E} = \frac{\vec{E}_{\text{ext}}}{\kappa} \]
where \(\kappa\) (or \(K\)) is the dielectric constant of the material.
Since \(\kappa\) is greater than 1, the internal electric field \(\vec{E}\) is less than the external electric field \(\vec{E}_{\text{ext}}\).
### 3. **Intuitive Understanding**
To summarize, the electric field inside a dielectric decreases due to polarization because:
- **Induced Charges:** The polarization in the dielectric induces bound charges that create an internal electric field opposing the external electric field.
- **Field Cancellation:** The internal field created by the polarization effectively reduces the net electric field within the dielectric compared to the external field applied to it.
This reduction in the internal electric field is a result of the dielectric’s response to the external field, where the dielectric material works to oppose the applied field through its polarization effects.
By reducing the effective electric field inside the dielectric, the dielectric reduces the overall energy stored in the electric field and allows the material to store more electrical energy in the form of polarization.
### 1. **Basic Concepts**
**Dielectric Material:** A dielectric is an insulating material that does not conduct electricity but can support an electrostatic field. When placed in an electric field, dielectrics exhibit polarization.
**Electric Field (\(\vec{E}\)):** This is the force per unit charge experienced by a charged particle in space due to other charges or fields.
**Polarization (\(\vec{P}\)):** Polarization refers to the alignment of electric dipoles in the dielectric material. When a dielectric is placed in an electric field, the positive and negative charges in the dielectric material slightly shift, creating an induced electric dipole moment per unit volume.
### 2. **Effect of Polarization on the Electric Field**
When a dielectric material is placed in an external electric field (\(\vec{E}_{\text{ext}}\)), it becomes polarized. Here's how this affects the electric field inside the dielectric:
#### a. **Induced Dipoles and Internal Field**
- **Polarization Charge:** The shifting of charges creates bound surface charges on the surface of the dielectric, which results in an internal electric field (\(\vec{E}_{\text{int}}\)) opposing the external field. This internal field is due to the dipole moments induced by the external electric field.
- **Opposing Field:** The induced dipole moments in the dielectric create an electric field that acts in the opposite direction to the external electric field. This is because the negative ends of the dipoles are oriented towards the positive side of the external field, and vice versa.
#### b. **Electric Displacement Field (\(\vec{D}\))**
The electric displacement field \(\vec{D}\) accounts for the effects of polarization:
\[ \vec{D} = \epsilon_0 \vec{E} + \vec{P} \]
where:
- \(\epsilon_0\) is the permittivity of free space,
- \(\vec{E}\) is the electric field inside the dielectric,
- \(\vec{P}\) is the polarization vector.
For a given external electric field \(\vec{E}_{\text{ext}}\), the relationship between the electric displacement field \(\vec{D}\) and \(\vec{E}_{\text{ext}}\) is:
\[ \vec{D} = \epsilon \vec{E}_{\text{ext}} \]
where \(\epsilon\) is the permittivity of the dielectric, which is higher than \(\epsilon_0\).
#### c. **Reduced Internal Electric Field**
The internal electric field \(\vec{E}\) within the dielectric material is related to the external field by:
\[ \vec{E} = \frac{\vec{E}_{\text{ext}}}{\kappa} \]
where \(\kappa\) (or \(K\)) is the dielectric constant of the material.
Since \(\kappa\) is greater than 1, the internal electric field \(\vec{E}\) is less than the external electric field \(\vec{E}_{\text{ext}}\).
### 3. **Intuitive Understanding**
To summarize, the electric field inside a dielectric decreases due to polarization because:
- **Induced Charges:** The polarization in the dielectric induces bound charges that create an internal electric field opposing the external electric field.
- **Field Cancellation:** The internal field created by the polarization effectively reduces the net electric field within the dielectric compared to the external field applied to it.
This reduction in the internal electric field is a result of the dielectric’s response to the external field, where the dielectric material works to oppose the applied field through its polarization effects.
By reducing the effective electric field inside the dielectric, the dielectric reduces the overall energy stored in the electric field and allows the material to store more electrical energy in the form of polarization.
The electric field inside a dielectric decreases due to polarization because of the way electric dipoles within the dielectric material respond to an external electric field. Let's explore this concept in detail:
### What is a Dielectric?
A **dielectric** is an insulating material that does not conduct electricity but can support an electric field. Examples of dielectrics include rubber, glass, mica, and certain plastics. Dielectrics are often used in capacitors and other electrical components to increase their capacitance.
### Understanding Polarization
**Polarization** in the context of dielectrics refers to the alignment of electric dipoles (molecules or atoms with positive and negative charges separated by a small distance) within the material when it is exposed to an external electric field.
1. **In the Absence of an Electric Field:**
- When no external electric field is applied, the dipoles in a dielectric material are randomly oriented due to thermal motion, resulting in no net dipole moment in any specific direction.
2. **When an External Electric Field is Applied:**
- When an external electric field (\(E_0\)) is applied, it exerts a force on the charges within the atoms or molecules. The positive charges (nuclei) experience a force in the direction of the field, while the negative charges (electrons) experience a force in the opposite direction.
- This causes the dipoles to align partially with the external electric field, resulting in **polarization** of the dielectric material. The dielectric material becomes polarized, meaning that positive and negative charges slightly shift in opposite directions, creating tiny induced dipoles throughout the material.
### How Polarization Affects the Electric Field
Due to polarization, the dielectric creates its own internal electric field (\(E_p\)) in the opposite direction to the external electric field (\(E_0\)). This opposing field reduces the net electric field (\(E\)) inside the dielectric.
\[
E = E_0 - E_p
\]
Here's how this happens in more detail:
1. **Formation of Bound Charges:**
- The alignment of dipoles within the dielectric material results in the formation of "bound" surface charges. On the surface facing the direction of the external electric field, negative bound charges appear. On the opposite surface, positive bound charges appear. These bound charges are fixed within the dielectric and cannot move freely like free charges in a conductor.
2. **Creation of an Internal Electric Field (\(E_p\)):**
- The bound charges create their own electric field, which opposes the external electric field. This internal electric field (\(E_p\)) is directed opposite to \(E_0\).
3. **Reduction of the Net Electric Field (\(E\)):**
- The opposing internal electric field (\(E_p\)) reduces the strength of the overall electric field inside the dielectric material. Therefore, the net electric field inside the dielectric is less than the applied electric field. The more the dielectric material polarizes, the stronger the opposing field it creates, and the greater the reduction in the net electric field.
### Dielectric Constant and Polarization
The degree to which a dielectric material can be polarized by an external electric field is characterized by its **dielectric constant** (relative permittivity), \( \varepsilon_r \). The dielectric constant is a measure of how effectively the material reduces the internal electric field. It is given by:
\[
\varepsilon_r = \frac{E_0}{E}
\]
Where:
- \(E_0\) is the external electric field.
- \(E\) is the reduced net electric field inside the dielectric.
For a given external electric field, the higher the dielectric constant, the greater the reduction in the electric field inside the material. This happens because a higher dielectric constant indicates that the material can polarize more strongly, thereby creating a more significant opposing internal electric field.
### Conclusion
In summary, the electric field inside a dielectric material decreases due to polarization because the induced dipoles within the dielectric create an internal electric field that opposes the external electric field. The stronger this polarization effect, the greater the reduction in the net electric field inside the dielectric. This phenomenon is fundamental in understanding the behavior of dielectric materials in capacitors and other electronic devices, where they are used to enhance performance by reducing the electric field and increasing the capacitance.
### What is a Dielectric?
A **dielectric** is an insulating material that does not conduct electricity but can support an electric field. Examples of dielectrics include rubber, glass, mica, and certain plastics. Dielectrics are often used in capacitors and other electrical components to increase their capacitance.
### Understanding Polarization
**Polarization** in the context of dielectrics refers to the alignment of electric dipoles (molecules or atoms with positive and negative charges separated by a small distance) within the material when it is exposed to an external electric field.
1. **In the Absence of an Electric Field:**
- When no external electric field is applied, the dipoles in a dielectric material are randomly oriented due to thermal motion, resulting in no net dipole moment in any specific direction.
2. **When an External Electric Field is Applied:**
- When an external electric field (\(E_0\)) is applied, it exerts a force on the charges within the atoms or molecules. The positive charges (nuclei) experience a force in the direction of the field, while the negative charges (electrons) experience a force in the opposite direction.
- This causes the dipoles to align partially with the external electric field, resulting in **polarization** of the dielectric material. The dielectric material becomes polarized, meaning that positive and negative charges slightly shift in opposite directions, creating tiny induced dipoles throughout the material.
### How Polarization Affects the Electric Field
Due to polarization, the dielectric creates its own internal electric field (\(E_p\)) in the opposite direction to the external electric field (\(E_0\)). This opposing field reduces the net electric field (\(E\)) inside the dielectric.
\[
E = E_0 - E_p
\]
Here's how this happens in more detail:
1. **Formation of Bound Charges:**
- The alignment of dipoles within the dielectric material results in the formation of "bound" surface charges. On the surface facing the direction of the external electric field, negative bound charges appear. On the opposite surface, positive bound charges appear. These bound charges are fixed within the dielectric and cannot move freely like free charges in a conductor.
2. **Creation of an Internal Electric Field (\(E_p\)):**
- The bound charges create their own electric field, which opposes the external electric field. This internal electric field (\(E_p\)) is directed opposite to \(E_0\).
3. **Reduction of the Net Electric Field (\(E\)):**
- The opposing internal electric field (\(E_p\)) reduces the strength of the overall electric field inside the dielectric material. Therefore, the net electric field inside the dielectric is less than the applied electric field. The more the dielectric material polarizes, the stronger the opposing field it creates, and the greater the reduction in the net electric field.
### Dielectric Constant and Polarization
The degree to which a dielectric material can be polarized by an external electric field is characterized by its **dielectric constant** (relative permittivity), \( \varepsilon_r \). The dielectric constant is a measure of how effectively the material reduces the internal electric field. It is given by:
\[
\varepsilon_r = \frac{E_0}{E}
\]
Where:
- \(E_0\) is the external electric field.
- \(E\) is the reduced net electric field inside the dielectric.
For a given external electric field, the higher the dielectric constant, the greater the reduction in the electric field inside the material. This happens because a higher dielectric constant indicates that the material can polarize more strongly, thereby creating a more significant opposing internal electric field.
### Conclusion
In summary, the electric field inside a dielectric material decreases due to polarization because the induced dipoles within the dielectric create an internal electric field that opposes the external electric field. The stronger this polarization effect, the greater the reduction in the net electric field inside the dielectric. This phenomenon is fundamental in understanding the behavior of dielectric materials in capacitors and other electronic devices, where they are used to enhance performance by reducing the electric field and increasing the capacitance.