Why electric field inside a dielectric is not zero?
2 Answers
The electric field inside a dielectric material is not zero due to the fundamental nature of dielectrics and how they respond to an applied electric field. To understand this, it's useful to delve into the behavior of dielectrics and the principles of electrostatics.
### What is a Dielectric?
A dielectric is an insulating material that, when placed in an electric field, becomes polarized. This means that the positive and negative charges within the dielectric align in response to the field, creating a polarization effect. Dielectrics are characterized by their ability to be polarized but do not conduct electric current like metals.
### Electric Field in a Dielectric
1. **Applied Electric Field**: When an external electric field \( \mathbf{E}_{\text{ext}} \) is applied to a dielectric material, it causes the positive and negative charges in the material to shift slightly. This results in the generation of an internal electric field due to the alignment of dipoles in the dielectric.
2. **Polarization**: The polarization \( \mathbf{P} \) of the dielectric is a measure of the dipole moment per unit volume. The polarization creates its own electric field \( \mathbf{E}_{\text{p}} \) that opposes the applied field. This opposing field is a result of the dielectric's internal charge separation.
3. **Net Electric Field**: The total electric field \( \mathbf{E}_{\text{total}} \) inside the dielectric is the vector sum of the applied field \( \mathbf{E}_{\text{ext}} \) and the field due to polarization \( \mathbf{E}_{\text{p}} \). Therefore, the electric field inside the dielectric is given by:
\[
\mathbf{E}_{\text{total}} = \mathbf{E}_{\text{ext}} - \frac{\mathbf{P}}{\epsilon_0}
\]
where \( \epsilon_0 \) is the permittivity of free space.
4. **Why the Field is Not Zero**: The internal electric field \( \mathbf{E}_{\text{total}} \) is not zero because:
- The polarization \( \mathbf{P} \) does not completely cancel out the applied field \( \mathbf{E}_{\text{ext}} \). Instead, it reduces the field.
- The degree of polarization depends on the material’s properties and the strength of the applied field.
- In a uniform applied field, the polarization is uniform, but in a real dielectric, imperfections and variations in material properties can lead to a non-zero net field.
### Mathematical Explanation
To be more precise, in a dielectric, the relationship between the electric displacement field \( \mathbf{D} \), the electric field \( \mathbf{E} \), and the polarization \( \mathbf{P} \) is given by:
\[
\mathbf{D} = \epsilon_0 \mathbf{E} + \mathbf{P}
\]
The electric field \( \mathbf{E} \) inside the dielectric is related to the displacement field \( \mathbf{D} \) by:
\[
\mathbf{E} = \frac{\mathbf{D} - \mathbf{P}}{\epsilon_0}
\]
In summary, the electric field inside a dielectric is not zero because the applied electric field is only partially countered by the polarization effect. The remaining field represents the effective internal electric field. This is a key aspect of dielectric materials and their interactions with electric fields.
### What is a Dielectric?
A dielectric is an insulating material that, when placed in an electric field, becomes polarized. This means that the positive and negative charges within the dielectric align in response to the field, creating a polarization effect. Dielectrics are characterized by their ability to be polarized but do not conduct electric current like metals.
### Electric Field in a Dielectric
1. **Applied Electric Field**: When an external electric field \( \mathbf{E}_{\text{ext}} \) is applied to a dielectric material, it causes the positive and negative charges in the material to shift slightly. This results in the generation of an internal electric field due to the alignment of dipoles in the dielectric.
2. **Polarization**: The polarization \( \mathbf{P} \) of the dielectric is a measure of the dipole moment per unit volume. The polarization creates its own electric field \( \mathbf{E}_{\text{p}} \) that opposes the applied field. This opposing field is a result of the dielectric's internal charge separation.
3. **Net Electric Field**: The total electric field \( \mathbf{E}_{\text{total}} \) inside the dielectric is the vector sum of the applied field \( \mathbf{E}_{\text{ext}} \) and the field due to polarization \( \mathbf{E}_{\text{p}} \). Therefore, the electric field inside the dielectric is given by:
\[
\mathbf{E}_{\text{total}} = \mathbf{E}_{\text{ext}} - \frac{\mathbf{P}}{\epsilon_0}
\]
where \( \epsilon_0 \) is the permittivity of free space.
4. **Why the Field is Not Zero**: The internal electric field \( \mathbf{E}_{\text{total}} \) is not zero because:
- The polarization \( \mathbf{P} \) does not completely cancel out the applied field \( \mathbf{E}_{\text{ext}} \). Instead, it reduces the field.
- The degree of polarization depends on the material’s properties and the strength of the applied field.
- In a uniform applied field, the polarization is uniform, but in a real dielectric, imperfections and variations in material properties can lead to a non-zero net field.
### Mathematical Explanation
To be more precise, in a dielectric, the relationship between the electric displacement field \( \mathbf{D} \), the electric field \( \mathbf{E} \), and the polarization \( \mathbf{P} \) is given by:
\[
\mathbf{D} = \epsilon_0 \mathbf{E} + \mathbf{P}
\]
The electric field \( \mathbf{E} \) inside the dielectric is related to the displacement field \( \mathbf{D} \) by:
\[
\mathbf{E} = \frac{\mathbf{D} - \mathbf{P}}{\epsilon_0}
\]
In summary, the electric field inside a dielectric is not zero because the applied electric field is only partially countered by the polarization effect. The remaining field represents the effective internal electric field. This is a key aspect of dielectric materials and their interactions with electric fields.