Trystan Casey
Electric displacement, also known as electric flux density, is a vector field that appears in Maxwell's equations. It is denoted by the letter 'D' and represents the aspect of an electric field associated with the presence of separated free electric charges. It is used to calculate the density of electric flux within a charged field and is particularly relevant when a dielectric is introduced into the apparatus. Dielectrics are insulating materials that do not have free or loosely bound electrons, and they are often polarised when introduced to an electric field. Electric displacement is the charge per unit area that would be displaced across a layer of conductor placed across an electric field.
| Characteristics | Values |
|---|---|
| Definition | Electric displacement is the charge per unit area that is displaced across a layer of conductor placed across an electric field. |
| Other names | Electric flux density, free charge surface density, auxiliary electric field, electric vector |
| Equation | D = ε0E + P (in the metre-kilogram-second or SI system); D = E + 4πP (in the centimetre-gram-second system) |
| SI unit | Coulomb per meter square (C m-2) |
| First known use | 1864, in James Clerk Maxwell's paper "A Dynamical Theory of the Electromagnetic Field" |
| Application | Electric displacement is used in the context of dielectric materials to find the response of the materials to the application of an electric field. |
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What You'll Learn
Electric displacement field
Electric displacement, denoted by D, is the charge per unit area that would be displaced across a layer of conductor placed across an electric field. It is also known as electric flux density. The SI unit of electric displacement is Coulomb per meter square (C m-2).
Electric displacement is used in the dielectric material to find the response of the materials on the application of an electric field E. In Maxwell’s equation, it appears as a vector field. It plays a major role in the physics of phenomena such as the capacitance of a material, the response of dielectrics to an electric field, how shapes can change due to electric fields in piezoelectricity or flexoelectricity, as well as the creation of voltages and charge transfer due to elastic strains.
The earliest known use of the term is from the year 1864, in James Clerk Maxwell's paper "A Dynamical Theory of the Electromagnetic Field". Maxwell introduced the term D, specific capacity of electric induction, in a form different from the modern and familiar notations. It was Oliver Heaviside who reformulated the complicated Maxwell's equations to the modern form.
In linear, homogeneous, isotropic media, ε is a constant. However, in linear anisotropic media it is a tensor, and in nonhomogeneous media it is a function of position inside the medium. It may also depend upon the electric field (nonlinear materials) and have a time-dependent response. Explicit time dependence can arise if the materials are physically moving or changing in time (e.g. reflections off a moving interface give rise to Doppler shifts).
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Electric flux density
The concept of electric flux density is important when dealing with boundaries between media with different permittivities. It is defined as the number of electric field lines per unit area. These field lines are a graphical representation of the field's strength and direction and have no physical meaning when considered in isolation.
In the metre-kilogram-second (mks) or SI system, the dimensions of electric flux density are charge per unit area, with units of coulombs per square metre (C/m^2). It is calculated as the product of the electric field E and the permittivity of a vacuum, ε0:
D = ε0 * E
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Polarization
Electric displacement, denoted by D, is the charge per unit area that is displaced across a layer of conductor placed across an electric field. It is also known as electric flux density. Electric displacement is used in the dielectric material to find the response of the materials on the application of an electric field E. In Maxwell’s equation, it appears as a vector field. The SI unit of electric displacement is Coulomb per meter square (C m-2).
The relationship between polarization and electric displacement can be observed in various scenarios. For example, in a parallel-plate capacitor, the space between the plates can be filled with dielectric materials, and the electric displacement in each slab can be calculated. The presence of dielectric materials increases the capacitance for a fixed plate size and separation. The electric displacement field in this context satisfies Gauss's law in a dielectric, where the displacement field is influenced by the permittivity of the material and the electric field.
Additionally, polarization can be frozen in certain materials, such as a bar electret, where there is no free charge. However, the inherent polarization gives rise to an electric field, demonstrating that the electric displacement field is not solely determined by the free charge. The electric field in such cases can be determined by considering the polarization density and boundary conditions, which then yield the bound charges and subsequently the electric field.
The concept of polarization also extends to materials without an inversion center, exhibiting piezoelectricity and permanent polarization. In other materials, spatial variations can break inversion symmetry, leading to polarization, known as the flexoelectric effect. Furthermore, external stimuli like magnetic fields can induce polarization in some materials through the magnetoelectric effect. These interactions between polarization and electric displacement play a significant role in understanding the behaviour of materials in electric and electromagnetic fields.
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Dielectric materials
> Vacuum permittivity is the value of absolute dielectric permittivity, i.e., it is the capability of the vacuum to permit electric field lines.
The electric displacement of a dielectric material can be calculated using the formula:
> D = ε0E + P
Where ε0 is vacuum permittivity, E is the electric field, and P is the polarization density. The SI unit of electric displacement is Coulombs per square meter.
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Electric displacement in Maxwell's equations
Electric displacement, denoted by D, is the charge per unit area that would be displaced across a layer of conductor placed across an electric field. It is also known as electric flux density. In Maxwell's equations, it appears as a vector field.
Maxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric and magnetic circuits. The equations provide a mathematical model for electric, optical, and radio technologies, such as power generation, electric motors, wireless communication, lenses, and radar. They describe how electric and magnetic fields are generated by charges, currents, and changes in the fields.
The original law of Ampère states that magnetic fields relate to electric current. Maxwell's addition states that magnetic fields also relate to changing electric fields, which he called the displacement current. The integral form states that electric and displacement currents are associated with a proportional magnetic field along any enclosing curve. The displacement current was introduced to the current in terms of Ampere's circuit law to make it logically consistent. It is defined in terms of the rate of change of the electric displacement field (D).
The publication of Maxwell's equations marked the unification of a theory for previously separately described phenomena: magnetism, electricity, light, and associated radiation. The symmetry that Maxwell introduced into his mathematical framework may not be immediately apparent. Faraday's law describes how changing magnetic fields produce electric fields. The displacement current results from a changing electric field and accounts for a changing electric field producing a magnetic field. The equations for the effects of both changing electric fields and changing magnetic fields differ in form only where the absence of magnetic monopoles leads to missing terms. This symmetry between the effects of changing magnetic and electric fields is essential in explaining the nature of electromagnetic waves.
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Frequently asked questions
Electric displacement is the charge per unit area that is displaced across a layer of conductor positioned across an electric field. It is also known as electric flux density.
The earliest known use of the term is from 1864, in James Clerk Maxwell's paper "A Dynamical Theory of the Electromagnetic Field". The term was later reformulated by Oliver Heaviside, who grouped Maxwell's complicated equations into a distinct set now known as the Maxwell-Heaviside equations.
Electric displacement calculates the density of electric flux within a charged field. It is used in dielectric materials to find the response of the materials when an electric field is applied.
The equation for electric displacement in a dielectric material is:
\begin{equation*}
\\oint D \\cdot d a=4 \\pi Q_f
\end{equation*}
The SI unit of electric displacement is Coulomb per meter square (Cm^-2).
