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# Chapter 23 Gauss's Law

## Electric Flux

The concept of flux describes how much of something goes through a given area. More formally, it is the dot product of a vector field within an area.…

## Calculation of Electric Flux

Consider the electric field of an oppositely charged, parallel-plate system and an imaginary box between those plates. Let the bottom face of the box…

## 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…

## 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…

## 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…

## Gauss's Law: Cylindrical Symmetry

A charge distribution has cylindrical symmetry if the charge density depends only upon the distance from the axis of the cylinder and does not vary…

## 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…

## Electric Field Inside a Conductor

When a conductor is placed in an external electric field, the free charges in the conductor redistribute and very quickly reach electrostatic…

## Charge on a Conductor

An interesting property of a conductor in static equilibrium is that extra charges on the conductor end up on its outer surface, regardless of where…

## Electric Field at the Surface of a Conductor

Consider a conductor in electrostatic equilibrium. The net electric field inside a conductor vanishes, and extra charges on the conductor reside on…

## 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…

## 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…

## Divergence and Curl of Electric Field

The divergence of a vector is a measure of how much the vector spreads out (diverges) from a point. For example, an electric field vector diverges…

## External Excitation of Neurons Using Electric and Magnetic Fields in One- and Two-dimensional Cultures

A neuron will fire an action potential when its membrane potential exceeds a certain threshold. In typical activity of the brain, this occurs as a…

## A Fabrication Method for Highly Stretchable Conductors with Silver Nanowires

Stretchable electronics are identified as a key technology for electronic applications in the next generation. One of the challenges in fabrication…

## Probing and Mapping Electrode Surfaces in Solid Oxide Fuel Cells

Solid oxide fuel cells (SOFCs) are potentially the most efficient and cost-effective solution to utilization of a wide variety of fuels beyond…

## Scalable Solution-processed Fabrication Strategy for High-performance, Flexible, Transparent Electrodes with Embedded Metal Mesh

Here, the authors report the embedded metal-mesh transparent electrode (EMTE), a new transparent electrode (TE) with a metal mesh completely embedded…

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