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Gauss's Law: Planar Symmetry01:27

Gauss's Law: Planar Symmetry

A planar symmetry of charge density is obtained when charges are uniformly spread over a large flat surface. In planar symmetry, all points in a plane parallel to the plane of charge are identical with respect to the charges. Suppose the plane of the charge distribution is the xy-plane, and the electric field at a space point P with coordinates (x, y, z) is to be determined. Since the charge density is the same at all (x, y) - coordinates in the z = 0 plane, by symmetry, the electric field at P...
Equipotential Surfaces and Field Lines01:29

Equipotential Surfaces and Field Lines

Electric potential can be pictorially represented as a three-dimensional surface. On such a surface, the electric potential is constant everywhere. The equipotential surface is always perpendicular to the electric field lines, and while it is three-dimensional, it can be treated as an equipotential line in a two-dimensional case. These equipotential lines are also always perpendicular to electric field lines. The term equipotential is often used as a noun, referring to an equipotential line or...
Gauss's Law01:07

Gauss's Law

If a closed surface does not have any charge inside where an electric field line can terminate, then the electric field line entering the surface at one point must necessarily exit at some other point of the surface. Therefore, if a closed surface does not have any charges inside the enclosed volume, then the electric flux through the surface is zero. What happens to the electric flux if there are some charges inside the enclosed volume? Gauss's law gives a quantitative answer to this question.
Gauss's Law: Spherical Symmetry01:26

Gauss's Law: Spherical Symmetry

A charge distribution has spherical symmetry if the density of charge depends only on the distance from a point in space and not on the direction. In other words, if the system is rotated, it doesn't look different. For instance, if a sphere of radius R is uniformly charged with charge density ρ0, then the distribution has spherical symmetry. On the other hand, if a sphere of radius R is charged so that the top half of the sphere has a uniform charge density ρ1 and the bottom half has a uniform...
Surface Tension01:24

Surface Tension

Surface tension is defined as the force per unit length (γ) acting along the surface of a liquid. It arises due to strong intermolecular forces of attraction. A molecule located inside the bulk of the liquid is surrounded by other molecules and experiences equal forces in all directions. However, a molecule at the surface experiences unbalanced forces because there are more neighboring molecules below than above. This creates a net inward force that pulls surface molecules toward the interior,...
Gauss's Law: Problem-Solving01:10

Gauss's Law: Problem-Solving

Gauss's law helps determine electric fields even though the law is not directly about electric fields but electric flux. In situations with certain symmetries (spherical, cylindrical, or planar) in the charge distribution, the electric field can be deduced based on the knowledge of the electric flux. In these systems, we can find a Gaussian surface S over which the electric field has a constant magnitude. Furthermore, suppose the electric field is parallel (or antiparallel) to the area vector...

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Related Experiment Video

Updated: May 18, 2026

Setting Limits on Supersymmetry Using Simplified Models
07:46

Setting Limits on Supersymmetry Using Simplified Models

Published on: November 15, 2013

Fermi surfaces in maximal gauged supergravity.

Oliver DeWolfe1, Steven S Gubser, Christopher Rosen

  • 1Department of Physics, 390 UCB, University of Colorado, Boulder, Colorado 80309, USA.

Physical Review Letters
|September 26, 2012
PubMed
Summary

We found Fermi surface singularities in black hole physics, indicating non-Fermi liquid behavior in dual quantum field theories. This suggests no stable quasiparticles exist, challenging conventional understanding.

Area of Science:

  • Theoretical Physics
  • Quantum Field Theory
  • Black Hole Physics
  • String Theory

Background:

  • Investigates extremal charged black hole geometries in maximal gauged supergravity.
  • Focuses on four and five-dimensional spacetimes.
  • Examines fermion fluctuations around these black hole solutions.

Purpose of the Study:

  • To derive and analyze fermion fluctuation equations in specific black hole backgrounds.
  • To identify signatures of Fermi surface singularities in dual conformal field theories (CFTs).
  • To characterize the nature of emergent fermionic behavior, including quasiparticle stability.

Main Methods:

  • Obtained fermion fluctuation equations for extremal charged black holes.

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Last Updated: May 18, 2026

Setting Limits on Supersymmetry Using Simplified Models
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Published on: November 15, 2013

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  • Analyzed solutions in four and five dimensions, considering massless and massive charged fermions.
  • Employed Luttinger calculations to probe charge-carrying properties.

    • Main Results:

    • Demonstrated Fermi surface singularities in dual CFTs at finite chemical potential.
    • Identified non-Fermi liquid behavior with scaling exponents less than one half.
    • Found no stable quasiparticles, though some excitations showed narrow widths.

    Conclusions:

    • The study reveals non-Fermi liquid behavior in holographic CFTs dual to charged black holes.
    • Results suggest that gauginos may be significant charge carriers in the five-dimensional case.
    • The findings challenge conventional condensed matter paradigms by exhibiting exotic fermionic states.