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covarient derivative of electromagnetic field tensor
I'm trying to prove the energy momentum tensor in curved spacetime for Electromagnetic field is Divergence-less directly(Without using general lie derivative method which can prove any energy momentum ...
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Vector identities equivalence under different coordinates
I've learned to represent curl, rot and Laplacian in the general form using scaling factors, Levi Civita symbol and delta.
I was asked to prove some general identities in vector calculus.
I was ...
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Positive Permutation Tensor
I have seen that one can make an operator with
$$
L^i=\epsilon^{ijk}x_{j}\partial_{k}
$$
But what if I want to make instead items that are sums, instead of differences. For instance
...
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How do I write the energy of a constant, uniform 2D charge distribution?
Let's consider a 2D electromagnetic field defined in a square domain $[0,\Lambda]^2$, with periodic boundary conditions, with a constant charge distribution, uniform all over the aforementioned ...
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Determine the tensor of contraint and deformation of a cube under compression
We have a cube under compression with dimension l1*l2*l3, is put between 2 rigid plates in the axis 1 (two plates block the deformation of the cube in thí axis), the cube is also put on a rigid plate, ...
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Invariants of a tensor [closed]
I asked (almost) the same question in the math exchange.
I'm teaching a course, and I need a simple and intuitive proof that the invariants of a matrix ($3\times3$, but it doesn't matter) can be ...
