# Units of Flux Density: Electric Field vs Displacement Vector

• gralla55
In summary, the displacement vector D = (e0)E + P is often referred to as "flux density" despite having units of C/m^2, which are different from the units for electric flux, Vm. This can lead to confusion, as it may seem like the two quantities are the same. However, after analyzing the dimensions using Gauß's law, it becomes clear that the displacement vector does indeed have units of C/m^2, similar to surface charge density.
gralla55
While I do understand the use for the displacement vector D = (e0)E + P, I don't quite understand why they label it as "flux density". The units for the displacement vector are C/m^2. The units for electric flux are Vm, so wouldn't electric flux density become Vm/m^2 = V/m which is just equal to the electric field?

edit: C/m^2 just looks like surface charge density...

For this reason, I hate the SI. It's totally unintuitive. Anyway, let's work through the dimensional analysis. According to Gauß's law, which reads in differential form
$$\vec{\nabla} \cdot \vec{D}=\rho,$$
where $\rho$ is the charge density (i.e., charge per unit volume), which has the SI unit $\mathrm{C}/\mathrm{m}^3$ (Coulomb per cubic metre). The Nabla operator is a differential operator wrt. to space coordinates and thus has the unit $1/\mathrm{m}$.

This implies that $\vec{D}$ has the unit $\mathrm{C}/\mathrm{m}^2$.

## 1. What is the difference between electric field and displacement vector?

Electric field and displacement vector are two different ways of measuring the strength of an electric field. Electric field is a vector quantity that represents the force exerted on a charged particle at a specific point in space. Displacement vector, on the other hand, is a vector quantity that represents the change in position of a charged particle as it moves through an electric field. In other words, electric field measures the strength of the field at a single point, while displacement vector measures the overall effect of the field on a charged particle.

## 2. How are electric field and displacement vector related?

Electric field and displacement vector are related through the concept of electric flux. Electric flux is a measure of the flow of electric field through a surface. It is calculated by multiplying the strength of the electric field by the area of the surface and the cosine of the angle between the electric field and the surface. The displacement vector is a measure of the change in electric flux over time. In other words, the displacement vector is the rate of change of electric flux.

## 3. What are the units of measurement for electric field and displacement vector?

The units of measurement for electric field are newtons per coulomb (N/C) or volts per meter (V/m). The units of measurement for displacement vector are coulombs (C) or meters (m). These units represent the amount of force or charge, respectively, at a specific point in space or over a certain distance.

## 4. How are electric field and displacement vector used in practical applications?

Electric field and displacement vector are used in many practical applications, including electronics, power generation and transmission, and medical equipment. In electronics, they are used to calculate the strength of electric fields in circuits. In power generation and transmission, they are used to measure the strength of electric fields in power lines. In medical equipment, they are used to measure the strength of electric fields in diagnostic and therapeutic devices.

## 5. Can electric field and displacement vector be measured directly?

Electric field and displacement vector cannot be measured directly, as they are vector quantities. However, they can be calculated using other measured quantities, such as charge and distance, and the appropriate mathematical formulas. Additionally, specialized equipment such as electric field meters and gaussmeters can be used to indirectly measure the strength of electric fields and displacement vectors.

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