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Related Concept Videos

Electrostatic Boundary Conditions in Dielectrics01:27

Electrostatic Boundary Conditions in Dielectrics

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When an electric field passes from one homogeneous medium to another, crossing the boundary between the two mediums imparts a discontinuity in the electric field. This results in electrostatic boundary conditions that depend on the type of mediums the field propagates through.
Consider a case where both the mediums across a boundary are two different dielectric materials. Recall that the electric field and electric displacement are proportional and related through the material's permittivity....
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Determining Electric Field From Electric Potential01:12

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The electric field and electric potential are related to each other. If the electric field at various points in the region of interest is known, it can be used to calculate the electric potential difference between any two points. Similarly, if the electric potential is known for various points, then it is possible to calculate the electric field.
In general, regardless of whether the electric field is uniform, it points in the direction of decreasing potential because the force on a positive...
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Electrostatic Boundary Conditions01:16

Electrostatic Boundary Conditions

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Consider an external electric field propagating through a homogeneous medium. When the electric field crosses the surface boundary of the medium, it undergoes a discontinuity. The electric field can be resolved into normal and tangential components. The amount by which the field changes at any boundary is given by the difference between the field components above and below the surface boundary.
The surface integral of an electric field is given by Gauss's law in integral form and is related to...
694
Finding Electric Potential From Electric Field01:13

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For a system of charges, it is easy to calculate the system's potential because potential is a scalar quantity. However, in some instances where calculating the electric field is more straightforward than finding the potential, the electric field is used to calculate the system's potential. For a positive charge, the electric field is radially outward, and the potential is positive at any finite distance from the positive charge. In such an electric field, the motion away from the...
4.8K
Electric Field of Parallel Conducting Plates01:16

Electric Field of Parallel Conducting Plates

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Gauss' law relates the electric flux through a closed surface to the net charge enclosed by that surface. Gauss's law can be applied to find the electric field and the charge enclosed in a region depending on its charge distribution.
Consider a cross-section of a thin, infinite conducting plate having a positive charge. For such a large thin plate, as the thickness of the plate tends to zero, the positive charges lie on the plate's two large faces. Without an external electric field, the...
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Electric Field at the Surface of a Conductor01:26

Electric Field at the Surface of a Conductor

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Consider a conductor in electrostatic equilibrium. The net electric field inside a conductor vanishes, and extra charges on the conductor reside on its outer surface, regardless of where they originate.
In the 19th century, Michael Faraday conducted the famous ice pail experiment to prove that the charges always reside on the surface of a conductor. The experimental set-up consists of a conducting uncharged container mounted on an insulating stand. The outer surface of the container is...
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Related Experiment Video

Updated: Oct 31, 2025

Fabrication of Gate-tunable Graphene Devices for Scanning Tunneling Microscopy Studies with Coulomb Impurities
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Screening in Graphene: Response to External Static Electric Field and an Image-Potential Problem.

Vyacheslav M Silkin1,2,3, Eugene Kogan4, Godfrey Gumbs5

  • 1Donostia International Physics Center (DIPC), Paseo de Manuel Lardizabal 4, E-20018 San Sebastián, Basque Country, Spain.

Nanomaterials (Basel, Switzerland)
|July 2, 2021
PubMed
Summary
This summary is machine-generated.

We studied how graphene sheets respond to electric fields using first-principles calculations. The induced charge density and its centroid were determined, impacting image-potential states in graphene.

Keywords:
electric fieldgrapheneimage potentialimage-plane positionimage-potential statesvalence charge density

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Area of Science:

  • Condensed Matter Physics
  • Materials Science
  • Quantum Chemistry

Background:

  • Graphene's unique electronic properties make it a candidate for advanced electronic devices.
  • Understanding graphene's response to external fields is crucial for device applications.

Purpose of the Study:

  • To investigate the response of a free-standing graphene sheet to an external perpendicular static electric field.
  • To determine the induced charge density distribution and its centroid.
  • To analyze the impact of the electric field on image-potential states.

Main Methods:

  • First-principles calculations
  • Pseudopotential density-functional theory (DFT) approach
  • Analysis of charge density distribution and centroid position

Main Results:

  • The charge density distribution induced by the electric field was determined.
  • The centroid of the induced extra density (zim) was found to be 1.048 Å at vanishing electric field.
  • The dependence of zim on the electric field strength was obtained.
  • A hybrid one-electron potential was constructed using the determined zim, leading to new image-potential state energies.

Conclusions:

  • The study provides a detailed understanding of graphene's electronic response to electric fields.
  • The calculated zim and its field dependence are key parameters for modeling graphene-based systems.
  • The findings contribute to the development of novel graphene electronic devices.