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jsmith12
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If I'm given the components of an electrical conductivity tensor, how can I work out the directions in which the current is biggest and the directions in which no current flows?
The only eigenvectors corresponding to eigenvalue 3 all satisfy x+ y+ z= 0. That means that there is a 2 dimensional "eigenspace" of covering the plane x+ y+ z= 0. The flow is the same in all directions on that plane.jsmith12 said:Ok thanks. But if I'm trying to work this out for the matrix
2 -1 -1
-1 2 -1
-1 -1 2
which has eigenvalues 0, 3, 3.
The 0 eigenvalue gives (1,1,1) so that's the direction of no flow, but with eigenvalue 3 you can get lots of different eigenvectors so is the flow greatest in all of those directions?
The electrical conductivity tensor is a mathematical representation of how a material conducts electricity in different directions. It describes the relationship between an applied electric field and the resulting electric current in three dimensions.
The electrical conductivity tensor can be measured using a technique called electrical impedance spectroscopy, which involves applying an alternating electric field to the material and measuring the resulting current. The measurements are then used to calculate the conductivity tensor components.
The electrical conductivity tensor is affected by various factors such as temperature, pressure, and the composition and structure of the material. It can also be influenced by external factors such as the presence of impurities or defects in the material.
The electrical conductivity tensor is an important parameter in materials science as it provides crucial information about the electrical properties of a material. It is used to understand and predict the behavior of materials in electronic and electrical devices, and is also a key factor in designing and optimizing new materials for specific applications.
The electrical conductivity tensor is a more comprehensive measure of a material's electrical conductivity compared to a single conductivity value. It takes into account the directional dependence of conductivity, providing a more detailed understanding of the material's behavior. The tensor can also vary with external factors, whereas the conductivity value is typically considered constant for a given material at a specific temperature and pressure.