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.

View More On Wikipedia.org
Recent contents Top users
  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...
Back
Top