What is Electromagnetic tensor: Definition and 21 Discussions

In electromagnetism, the electromagnetic tensor or electromagnetic field tensor (sometimes called the field strength tensor, Faraday tensor or Maxwell bivector) is a mathematical object that describes the electromagnetic field in spacetime. The field tensor was first used after the four-dimensional tensor formulation of special relativity was introduced by Hermann Minkowski. The tensor allows related physical laws to be written very concisely.

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  1. jv07cs

    I 3+1 split of the Electromagnetic Tensor and Maxwell's Equations

    I'm currently studying the covariant formulation of electromagnetism for a research project I'm doing and I'm a bit a stuck on how to perform the 3+1 split of the Electromagnetic Field Tensor and Maxwell's Equations. I understand that a 3+1 split of a four-vector consists of separating the...
  2. P

    A Why electromagnetic tensor (Faraday 2-form) is exact? (and not closed)

    Following from Wikipedia, the covariant formulation of electromagnetic field involves postulating an electromagnetic field tensor(Faraday 2-form) F such that F=dA where A is a 1-form, which makes F an exact differential form. However, is there any specific reason for expecting F to be exact...
  3. L

    I Proving Antisymmetry of Electromagnetic Field Tensor with 4-Force

    I've already made a post about this topic here, but I realized that I didn't understand the explanation on that post. in Chapter 7 of Rindler's book on relativity, in section about electromagnetic field tensor, he states that _and introducing a factor 1/c for later convenience, we can ‘guess’...
  4. T

    A Evaluating Matrix Spin Dependent Term in Dirac Quadratic Equation

    I derive the quadratic form of Dirac equation as follows $$\lbrace[i\not \partial-e\not A]^2-m^2\rbrace\psi=\lbrace\left( i\partial-e A\right)^2 + \frac{1}{2i} \sigma^{\mu\nu}F_{\mu \nu}-m^2\rbrace\psi=0$$ And I need to find the form of the spin dependent term to get the final expression $$g...
  5. Andrea B DG

    A Electromagnetic tensor and time reversal

    Consider equation (2.7.8) page 42 in the book Gravitation and Cosmology by Weinberg F' αβ = Λαγ Λβδ Fγδ Now consider the time reversal Lorenz transformation Λμν = 0 if μ ≠ ν, 1 if μ = ν = 1..3 and -1 if μ = ν = 0 then F' 00 = 0 F' 0i = -F 0i F' ij = F ij Using equation (2.7.5) of the same book...
  6. A

    Electromagnetic Tensor: Calculating $\det{F^{\mu}}_\nu$

    Homework Statement Given an electromagnetic tensor ##F^{\mu\nu}##, showing that: $$\det{F^{\mu}}_\nu=-(\vec{B}\cdot\vec{E})^2$$ Homework Equations The Attempt at a Solution I had only the (stupid) idea of writing explictly the matrix associated with the electromagnetic tensor and calculating...
  7. Mihai_B

    I Solve Electromagnetic Field Acting on Charged Particle

    Can anyone help me find any mistake in this expansion ? (I've asked it also in other places but I got no answer)) Pα= e Fαβ Uβ c = speed of light m = "rest" mass e = charge a = sqr(1 - v2/c2) v2 = vx2 + vy2 + vz2 dτ = dt a (proper time) momentum 4 vector : Pα = [mc/a , mvx/a , mvy/a ...
  8. S

    Solving Electromagnetic Tensor & B-Field

    Hello, first off, I'm not sure if I put this question in the right place so sorry about that. Given Bi = 1/2 εijk Fjk how would you find F in terms of B? I think you multiply through by another Levi-Civita, but then I don't know what to do after that. Any help would much appreciated.
  9. tomdodd4598

    Electromagnetic Tensor in (-+++) Convention

    Hi there, Over the last couple of weeks, I have been learning about the relativistic description of electromagnetism through Leonard Susskind's Theoretical Minimum lectures, and although I have managed to follow it, there are some parts which I am becoming increasingly confused by, not helped...
  10. itssilva

    Electromagnetic tensor and energy

    From introductory courses on EM, I was given 'sketchy' proofs that, in a EM field in vacuum, magnetic energy density is B² and electric energy density is E² (bar annoying multiplication factors; they just get under my skin, I'll skip them all in the following). Other facts of life: -FμνFμν, the...
  11. TrickyDicky

    Electromagnetic tensor and restricted Lorentz group

    How exactly is the EM field tensor related to the proper orthochronous Lorentz group?
  12. C

    Constructing the electromagnetic tensor from a four-potential

    *Edit: I noticed I may have posted this question on the wrong forum... if this is the case, could you please move it for me instead of deleting? thanks! :) Hello, I am having problems on building my electromagnetic tensor from a four-potential. I suspect my calculations are not right. Here are...
  13. G

    How is the electromagnetic tensor derived?

    I understand that the EM tensor is a way of expressing the electromagnetic field in a frame invariant way, but how is it derived? Please use the (-+++) convention as I mostly use that.
  14. W

    Relativistic force and electromagnetic tensor follow up

    A while back (thread) you guys helped me understand why \tilde{F}=m\frac{d\gamma\tilde{v}}{dt} (3-vectors) as it follows from \bar{F}=q\Psi\bar{v} (4-vectors) and \tilde{F}=q(\tilde{E}+\tilde{v}\times \tilde{B}) (3-vectors). However, I had the impression that one also uses...
  15. S

    Electromagnetic Tensor: Questions & Answers

    dear all, I have a question about Electromagnetic field tensor. As I was reading introduction to relativity by Hobson, I saw this sentence: "in order that the rest mass of a particle is not altered by the action of the erforce we require the latter to be a pure force, so: u.f=0 1) what does it...
  16. N

    Electromagnetic tensor in cylindrical coordinates

    I can find the metric tensor in cylindrical coordinates to be [1,-1,-1/r^2,-1] but how about the electromagnetic field tensor and thus the energy stress tensor? Is it just change the Ex,Ey,Ez to Eρ,Eθ,Ez? Is FσρFσρ still equal to 2(B^2-E^2)
  17. B

    Using the transform of the electromagnetic tensor F between frames, verify that

    Homework Statement Using the transform of the electromagnetic tensor F between frames, F'=RFR^{T} verify that: i) the perpendicular component of the magnetic field in the frame, S', moving with velocity v with respect to the frame S, can be found from the transform of B_{\bot} in S...
  18. G

    Electromagnetic Tensor: Vector Space Explained

    Hey, does anoyone of you know to which vector space the electromagnetic tensor belongs to? thank you for your ideas...
  19. V

    Lorentz transformation in four dimensions of the electromagnetic tensor

    Homework Statement Given: electromagnetic tensor F(superscript)uv: electromagnetic tensor F' after the lorentz transformation: [ 0 -Ex -gamma(Ey-VBz/c) -gamma(Ez-VBy/c) Ex 0...
  20. V

    Electromagnetic Tensor:Relativity,E&B Vectors,Equations,Poisson Eq.

    I understand that after writing down this: F^{ \mu v} = \partial^{\mu} A^v- \partial^v A^{\mu} We can get a nice matrix connecting E and B vectors. But I just wonder what we need this matrix for? I am a little bit confused about all this relativity in electromagnetism... And another...
  21. P

    Electromagnetic tensor - invariant

    Homework Statement Hi, I have to calculate the invariant: \tilde{F}^{\mu \nu} \, F_{\mu \nu} where F is the electromagnetic field tensor and \tilde{F} the dual one. Homework Equations First, the contravariant components of the electromagnetic field tensor are given by...