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Gauss's Law: Problem-Solving

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...

Electric Field of a Non Uniformly Charged Sphere

Electric Field of a Non Uniformly Charged Sphere

Gauss's law states that the electric flux through any closed surface equals the net charge enclosed within the surface. This law is beneficial for determining the expressions for the electric field for a particular charge distribution if the electric flux is known.
Consider a non-uniformly charged sphere, for which the density of charge depends only on the distance from a point in space and not on the direction. Such a sphere has a spherically symmetrical charge distribution. Here, the electric...

The Pauli Exclusion Principle

The Pauli Exclusion Principle

The arrangement of electrons in the orbitals of an atom is called its electron configuration. We describe an electron configuration with a symbol that contains three pieces of information:

Second Uniqueness Theorem

Second Uniqueness Theorem

Consider a region consisting of several individual conductors with a definite charge density in the region between these conductors. The second uniqueness theorem states that if the total charge on each conductor and the charge density in the in-between region are known, then the electric field can be uniquely determined.
In contrast, consider that the electric field is non-unique and apply Gauss's law in divergence form in the region between the conductors and the integral form to the surface...

Gauss's Law

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.

Electric Field of Parallel Conducting Plates

Electric Field of Parallel Conducting Plates

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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Related Experiment Video

Updated: Apr 25, 2026

Probing C84-embedded Si Substrate Using Scanning Probe Microscopy and Molecular Dynamics

Probing C84-embedded Si Substrate Using Scanning Probe Microscopy and Molecular Dynamics

Published on: September 28, 2016

Probing hidden sectors with Stückelberg U(1) gauge fields.

Wan-Zhe Feng¹, Gary Shiu², Pablo Soler²

¹Center for Fundamental Physics and Institute for Advanced Study, Hong Kong University of Science and Technology, Hong Kong and Max-Planck-Institut für Physik (Werner-Heisenberg-Institut), 80805 München, Germany.

Physical Review Letters

|August 23, 2014

Summary

We introduce a new framework for hidden sector interactions via Stückelberg U(1) gauge fields. This model broadens Z

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Setting Limits on Supersymmetry Using Simplified Models

Setting Limits on Supersymmetry Using Simplified Models

Published on: November 15, 2013

Area of Science:

Particle Physics
Cosmology
String Theory

Background:

The Standard Model of particle physics describes visible matter but does not account for dark matter or other hidden sectors.
Existing models for mediating interactions between visible and hidden sectors, such as Z' mediation, often face limitations.

Purpose of the Study:

To propose a novel theoretical framework for interactions between visible matter and a hidden sector.
To explore the potential for broadening the choices of Z' bosons without introducing exotic matter.
To investigate the possibility of significant tree-level interactions between the visible and hidden sectors.

Main Methods:

Utilizing a theoretical framework based on mass mixings of Stückelberg U(1) gauge fields.
Analyzing the phenomenological features of string theory embeddings of the proposed scenario.

Main Results:

The proposed framework allows for a wider selection of Z' bosons compared to other mediation scenarios.
The model avoids the introduction of unwanted exotic matter, even with broadened Z' choices.
Sizable tree-level interactions between the visible and hidden sectors are possible within this framework.

Conclusions:

The proposed Stückelberg U(1) gauge field framework offers an appealing alternative for mediating interactions between visible and hidden sectors.
This approach provides greater flexibility in model building and potentially resolves some limitations of existing mediation scenarios.
Further investigation into string theory embeddings can illuminate the phenomenological consequences of this model.