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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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