Electric Displacement Field

In summary, the electric displacement field is a concept that is particularly useful in understanding the behavior of a capacitor. It involves a displacement current that flows through the capacitor to maintain Kirchhoff's first rule, and is related to the rate of change of the electric displacement field. This concept is important in the Ampére-Maxwell law and helps to explain the movement of free charge in a capacitor.
  • #1
Vanush
25
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Can someone please post a problem/situation outlining the motivation / usefulness of the electric displacement field? (Particularly with a capacitor) I'm having trouble understanding the concept and information is sparse on the internet.
 
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  • #2
Vanush said:
Can someone please post a problem/situation outlining the motivation / usefulness of the electric displacement field? (Particularly with a capacitor) I'm having trouble understanding the concept and information is sparse on the internet.

Hi Vanush! :smile:

For electric displacement field in a capacitor, this (from the PF Library) may help:

Displacement current:

No current ever flows through a functioning capacitor.

But while a capacitor is charging or discharging (that is, neither at zero nor maximum charge), current is flowing round the circuit joining the plates externally, and so there would be a breach of Kirchhoff's first rule (current in = current out at any point) at each plate, if only ordinary current were used, since there is ordinary current in the circuit on one side of the plate, but not in the dielectric on the other side.

Accordingly, a displacement current is deemed to flow through the capacitor, restoring the validity of Kirchhoff's first rule:

[tex]I\ =\ C\frac{dV}{dt}[/tex]

and this linear displacement current [itex]I[/itex] (which might better be called the flux current or free flux current) is the rate of change of the flux (field strength times area) of the electric displacement field [itex]D[/itex]:

[tex]I\ =\ A\,\widehat{\bold{n}}\cdot\frac{\partial\bold{D}}{\partial t}\ =\ A\,\frac{\partial D}{\partial t}\ =\ C\frac{dV}{dt}[/tex]

which appears in the Ampére-Maxwell law (one of Maxwell's equations in the free version):

[tex]\nabla\,\times\,\bold{H}\ =\ \bold{J}_f\ +\ \frac{\partial\bold{D}}{\partial t}[/tex]

Note that the displacement alluded to in the displacement current across a capacitor is of free charge, and is non-local, since it alludes to charge being displaced from one plate to the other, which is a substantial distance compared with the local displacement of bound charge in, for example, the presence of a polarisation field.
 
  • #3


The electric displacement field is a fundamental concept in electromagnetism that describes the ability of a material to store and transmit electric charges. It is represented by the symbol D and is defined as the electric flux per unit area of a material.

One way to understand the motivation and usefulness of the electric displacement field is by considering a capacitor. A capacitor is a device that stores electric charge and consists of two parallel plates separated by a dielectric material. When a voltage is applied to the capacitor, one plate becomes positively charged and the other becomes negatively charged. This creates an electric field between the plates, which is responsible for the storage of charge.

The electric displacement field helps us understand the behavior of the electric field inside the dielectric material. It is defined as the sum of the electric field and the polarization of the material, which is the induced dipole moment in the material due to the applied electric field. In other words, the electric displacement field takes into account the contribution of the material to the overall electric field.

In the case of a capacitor, the electric displacement field is particularly useful in understanding how the dielectric material affects the capacitance of the device. The capacitance is a measure of the ability of a capacitor to store charge and is directly proportional to the electric displacement field. This means that by changing the properties of the dielectric material, we can manipulate the electric displacement field and therefore, the capacitance of the capacitor.

Furthermore, the electric displacement field is also important in analyzing the behavior of capacitors in different types of circuits. For example, in AC circuits, the electric displacement field takes into account the time-varying behavior of the electric field and polarization, which affects the overall impedance and power dissipation of the capacitor.

In summary, the electric displacement field is a crucial concept in understanding the behavior of electric fields in materials, particularly in capacitors. It helps us analyze and manipulate the properties of capacitors, making it a valuable tool in various applications such as in electronic devices and power systems.
 

1. What is an electric displacement field?

The electric displacement field (D) is a vector field that describes the movement of electric charges through a material. It is related to the electric field (E) by the equation D = ε0E + P, where ε0 is the permittivity of free space and P is the polarization of the material.

2. How is the electric displacement field related to the electric field?

The electric displacement field is related to the electric field through the equation D = ε0E + P. This means that the electric field is the sum of two components: the electric field in free space (ε0E) and the effects of the polarization of the material (P).

3. What is the significance of the electric displacement field?

The electric displacement field is an important concept in electromagnetism as it helps us understand how electric charges move through different materials. It is also used in the study of dielectric materials and their behavior in electric fields.

4. How is the electric displacement field measured?

The electric displacement field is a vector quantity and is typically measured in units of coulombs per square meter (C/m^2). It can be measured using instruments such as a Gaussmeter or by calculating it using the equation D = ε0E + P.

5. What are some real-world applications of the electric displacement field?

The electric displacement field is used in various applications, such as in the design of capacitors, in the study of dielectric materials, and in the development of electronic devices. It is also important in understanding the behavior of electromagnetic waves in different materials and in the study of electric fields in living organisms.

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