What is rate of change of electric displacement called?
2 Answers
The rate of change of electric displacement is called the **"displacement current."**
To break it down a bit:
1. **Electric Displacement (D)**: This is a vector field used in electromagnetism to describe the effect of free and bound charges in a medium. It's related to the electric field (\(E\)) and the polarization (\(P\)) of the material by the relation \( \mathbf{D} = \epsilon_0 \mathbf{E} + \mathbf{P} \), where \(\epsilon_0\) is the permittivity of free space.
2. **Displacement Current (J_d)**: In Maxwell's equations, the displacement current density is introduced to account for the changing electric field in situations where there is no actual current flow. It's given by \( \mathbf{J_d} = \frac{\partial \mathbf{D}}{\partial t} \). This term ensures that the continuity equation for electric current is satisfied in cases of time-varying fields, and it plays a crucial role in describing the behavior of electromagnetic waves and fields.
The concept of displacement current was introduced by James Clerk Maxwell in the 19th century to extend Ampère's Law to include changing electric fields, thereby helping to unify the laws of electricity and magnetism into what we now call Maxwell's equations.
To break it down a bit:
1. **Electric Displacement (D)**: This is a vector field used in electromagnetism to describe the effect of free and bound charges in a medium. It's related to the electric field (\(E\)) and the polarization (\(P\)) of the material by the relation \( \mathbf{D} = \epsilon_0 \mathbf{E} + \mathbf{P} \), where \(\epsilon_0\) is the permittivity of free space.
2. **Displacement Current (J_d)**: In Maxwell's equations, the displacement current density is introduced to account for the changing electric field in situations where there is no actual current flow. It's given by \( \mathbf{J_d} = \frac{\partial \mathbf{D}}{\partial t} \). This term ensures that the continuity equation for electric current is satisfied in cases of time-varying fields, and it plays a crucial role in describing the behavior of electromagnetic waves and fields.
The concept of displacement current was introduced by James Clerk Maxwell in the 19th century to extend Ampère's Law to include changing electric fields, thereby helping to unify the laws of electricity and magnetism into what we now call Maxwell's equations.
The rate of change of electric displacement is called the **electric displacement current**.
In Maxwell's equations, the electric displacement current density \( \mathbf{J}_d \) is given by:
\[ \mathbf{J}_d = \frac{\partial \mathbf{D}}{\partial t} \]
where \( \mathbf{D} \) is the electric displacement field.
The electric displacement field \( \mathbf{D} \) is defined as:
\[ \mathbf{D} = \varepsilon \mathbf{E} \]
where \( \varepsilon \) is the permittivity of the material and \( \mathbf{E} \) is the electric field.
The concept of electric displacement current was introduced by James Clerk Maxwell to account for the changing electric field in his modified form of Ampère's law. It allows for the continuity of current in situations where the electric field changes with time, such as in capacitors where the electric field changes as a function of time, but there is no physical movement of charge through the gap between the plates.
In Maxwell's equations, the electric displacement current density \( \mathbf{J}_d \) is given by:
\[ \mathbf{J}_d = \frac{\partial \mathbf{D}}{\partial t} \]
where \( \mathbf{D} \) is the electric displacement field.
The electric displacement field \( \mathbf{D} \) is defined as:
\[ \mathbf{D} = \varepsilon \mathbf{E} \]
where \( \varepsilon \) is the permittivity of the material and \( \mathbf{E} \) is the electric field.
The concept of electric displacement current was introduced by James Clerk Maxwell to account for the changing electric field in his modified form of Ampère's law. It allows for the continuity of current in situations where the electric field changes with time, such as in capacitors where the electric field changes as a function of time, but there is no physical movement of charge through the gap between the plates.