The electric field intensity (E) due to an electric dipole at different positions can be described as follows:
1. **Axial Position:**
- At the axial position of an electric dipole, the point of interest is located along the axis of the dipole, some distance away from the dipole's center.
- The electric field intensity at the axial position (E_axial) is given by the formula:
E_axial = (1 / 4πε₀) * [2p / r³]
- In this formula, ε₀ represents the vacuum permittivity, p is the magnitude of the dipole moment, and r is the distance from the center of the dipole to the point where you're measuring the electric field.
- The electric field at the axial position is directly proportional to the inverse cube of the distance (r³) from the dipole.
2. **Coaxial Position:**
- At the coaxial position of an electric dipole, the point of interest is located along the same axis as the dipole but inside the dipole itself, within the region defined by the dipole's length.
- The electric field intensity at the coaxial position (E_coaxial) inside the dipole is also given by a similar formula:
E_coaxial = (1 / 4πε₀) * [p / r³]
- Again, ε₀ represents the vacuum permittivity, p is the magnitude of the dipole moment, and r is the distance from the center of the dipole to the point where you're measuring the electric field.
- The electric field at the coaxial position is directly proportional to the inverse cube of the distance (r³) from the dipole, but it is half the strength of the electric field at the axial position for the same distance (r).
In summary, the electric field intensity due to an electric dipole varies with the position relative to the dipole. At the axial position, it is stronger and directed along the axis, while at the coaxial position within the dipole, it is weaker and also directed along the axis but in the opposite direction to the axial field. These formulas are valid in vacuum or air; for other materials, you would consider the appropriate permittivity (ε) of the medium.
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Answer:
The electric field intensity (E) due to an electric dipole at different positions can be described as follows:
1. **Axial Position:**
- At the axial position of an electric dipole, the point of interest is located along the axis of the dipole, some distance away from the dipole's center.
- The electric field intensity at the axial position (E_axial) is given by the formula:
E_axial = (1 / 4πε₀) * [2p / r³]
- In this formula, ε₀ represents the vacuum permittivity, p is the magnitude of the dipole moment, and r is the distance from the center of the dipole to the point where you're measuring the electric field.
- The electric field at the axial position is directly proportional to the inverse cube of the distance (r³) from the dipole.
2. **Coaxial Position:**
- At the coaxial position of an electric dipole, the point of interest is located along the same axis as the dipole but inside the dipole itself, within the region defined by the dipole's length.
- The electric field intensity at the coaxial position (E_coaxial) inside the dipole is also given by a similar formula:
E_coaxial = (1 / 4πε₀) * [p / r³]
- Again, ε₀ represents the vacuum permittivity, p is the magnitude of the dipole moment, and r is the distance from the center of the dipole to the point where you're measuring the electric field.
- The electric field at the coaxial position is directly proportional to the inverse cube of the distance (r³) from the dipole, but it is half the strength of the electric field at the axial position for the same distance (r).
In summary, the electric field intensity due to an electric dipole varies with the position relative to the dipole. At the axial position, it is stronger and directed along the axis, while at the coaxial position within the dipole, it is weaker and also directed along the axis but in the opposite direction to the axial field. These formulas are valid in vacuum or air; for other materials, you would consider the appropriate permittivity (ε) of the medium.