What is the unit of electric flux density D?
The Correct Answer and Explanation is :
The unit of electric flux density ( \mathbf{D} ) is the coulomb per square meter (C/m²) in the International System of Units (SI).
Explanation:
Electric flux density, also known as the electric displacement field, is a vector field that represents the distribution of electric charge in a material, especially in the presence of dielectric materials. It describes how electric field lines are distributed through space, and it accounts for both the free charge in a material and the polarization due to bound charges.
Mathematically, the electric flux density ( \mathbf{D} ) is defined as:
[
\mathbf{D} = \epsilon_0 \mathbf{E} + \mathbf{P}
]
where:
- ( \mathbf{E} ) is the electric field,
- ( \epsilon_0 ) is the permittivity of free space,
- ( \mathbf{P} ) is the polarization of the material.
In SI units:
- The electric field ( \mathbf{E} ) has units of volts per meter (V/m), which is equivalent to newtons per coulomb (N/C).
- The polarization ( \mathbf{P} ) has units of coulombs per square meter (C/m²).
In vacuum, the electric flux density ( \mathbf{D} ) is related to the electric field ( \mathbf{E} ) by the permittivity of free space ( \epsilon_0 ) (approximately ( 8.85 \times 10^{-12} \, \text{C}^2/\text{N·m}^2 )).
When there is no material (vacuum), the electric flux density is simply proportional to the electric field:
[
\mathbf{D} = \epsilon_0 \mathbf{E}
]
Thus, since ( \mathbf{E} ) is measured in N/C and ( \epsilon_0 ) is in C²/N·m², the electric flux density ( \mathbf{D} ) has the unit of C/m².
This unit makes sense because it describes how much charge is “flowing” through a given area per unit time.