What is maxwell stress: Definition and 25 Discussions

The Maxwell stress tensor (named after James Clerk Maxwell) is a symmetric second-order tensor used in classical electromagnetism to represent the interaction between electromagnetic forces and mechanical momentum. In simple situations, such as a point charge moving freely in a homogeneous magnetic field, it is easy to calculate the forces on the charge from the Lorentz force law. When the situation becomes more complicated, this ordinary procedure can become impractically difficult, with equations spanning multiple lines. It is therefore convenient to collect many of these terms in the Maxwell stress tensor, and to use tensor arithmetic to find the answer to the problem at hand.
In the relativistic formulation of electromagnetism, the Maxwell's tensor appears as a part of the electromagnetic stress–energy tensor which is the electromagnetic component of the total stress–energy tensor. The latter describes the density and flux of energy and momentum in spacetime.

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  1. milkism

    Maxwell Stress components of the energy-stress-momentum tensor

    Question: Solution: I need help with the last part. I think my numerical factors are incorrect, even if I add the last term it will get worse. What have I done wrong, or is there a better way to deal with this?
  2. C

    A Perturbation of Maxwell stress from voltage distribution

    I have a voltage distribution ##V(x,y) = V_{dc}(x,y)+ V_{ac}(x,y) \cos(\omega t)##, I have derived the Matrix e. But I do not know how to extract it from the voltage, meaning I do not know how to find ##E_{x0} , E_{y0}, \delta E_{x}, \delta E_{y}## in terms of ##V_{dc}(x,y), V_{ac}(x,y)##...
  3. JD_PM

    Understanding the Maxwell Stress Tensor

    The elecromagnetic force can be expressed using the Maxwell Stress Tensor as: $$\vec F = \oint_{s} \vec T \cdot d \vec a - \epsilon \mu \frac{\partial }{\partial t} \oint_{V} \vec S d\tau $$ (How can I make the double arrow for the stress tensor ##T##?) In the static case, the second term...
  4. M

    Maxwell Stress Tensor: Engineering Question Answered

    Hello! I was talking with a friend today about electrical motors and we started talking about theoretical designs. One question came up which was could the Maxwell Stress Tensor be used to calculate the torque on a rotor of a motor where the airgap is held constant and the magnetic circuit...
  5. Another

    Help with Maxwell stress tensor

    << Mentor Note -- OP has been reminded to use the Homework Help Template when posting schoolwork questions >> my think if ## \hat{r} = \sin(θ) \cos( φ) \hat{x} +\sin(θ) \sin( φ) \hat{y} +\cos(θ) \hat{z} ## ## da = R^2 \sin(θ) dθdφ \hat{r} = da_{x} \hat{x} + da_{x} \hat{y} + da_{z} \hat{z}##...
  6. C

    Continuum mechanical analogous of Maxwell stress tensor

    Maxwell stress tensor ##\bar{\bar{\mathbf{T}}}## in the static case can be used to determine the total force ##\mathbf{f}## acting on a system of charges contanined in the volume bounded by ##S## $$ \int_{S} \bar{\bar{\mathbf{T}}} \cdot \mathbf n \,\,d S=\mathbf{f}= \frac{d}{dt} \mathbf...
  7. fluidistic

    Maxwell stress tensor to calculate force (EM)

    Homework Statement A sphere with dielectric constant ##\varepsilon## and radius R is placed inside a homogenous external electric field ##\vec E_0##. The sphere is divided in 2 hemispheres such that their common interface is orthogonal to the external field. Using the energy-momentum tensor...
  8. R

    Calculating Force using the Maxwell Stress Tensor

    Homework Statement Calculate the force of magnetic attraction between the northern and southern hemispheres of a uniformly charged spinning spherical shell, with radius R, angular velocity ω, and surface charge density σ. Use the Maxwell Stress TensorHomework Equations F=\oint \limits_S \...
  9. S

    Maxwell Stress Tensor -> Force between magnets and perfect iron

    (this is not a hw) Assume you have a magnet of dimensions x_m, h_m, remanent flux density Br, and coercive field density Hc. The magnet is placed in a magnetic "C" structure (perfect iron) such that it is connected on one side but there is an airgap on the other side. xxxxxxxx xx... xx...
  10. TrickyDicky

    Is the Maxwell stress tensor a true stress?

    Should it be added to the Cauchy stress to calculate a "total stress", or it doesn't have such a physical interpretation as a surface force(EM field force is usually considered more of a "body force")? Certainly when the MST was first derived before aether theories were made superfluous by...
  11. D

    Maxwell stress tensor in different coordinate system

    Hi guys, I would like to know if the answer given to this thread is correct https://www.physicsforums.com/showthread.php?t=457405 I got the same doubt, is the expression for the tensor given in cartesian coordinates or is it general to any orthogonal coordinate system? Thanks in advance
  12. P

    Maxwell Stress Tensor in the absence of a magnetic field

    I'm having some trouble calculating the stress tensor in the case of a static electric field without a magnetic field. Following the derivation on Wikipedia, 1. Start with Lorentz force: \mathbf{F} = q(\mathbf{E} + \mathbf{v}\times\mathbf{B}) 2. Get force density \mathbf{f} =...
  13. H

    Maxwell stress tensor for a nonlinear media

    Hi all, It seems to me that the derivation of Maxwell stress tensor is independent of the permeability of the media or the nonliterary of its B-H relation. By this I mean that we use μ0 in the equations rather than μ. Would you please confirm that?
  14. H

    Maxwell Stress Tensor: Application & Force Calculation

    Hello everyone, I have a confusion about the application of Maxwell stress tensor: I have read some materials about Maxwell stress tensor and its application in calculating electromagnetic force on a body. To this end, a closed surface is assumed around the body and a surface integral on...
  15. A

    Direction of the Maxwell stress tensor

    Homework Statement Show that in vacuum the pressure tensor of a (complex) plane electromagnetic wave only has a contribution for both directions in this bivector being along the direction of motion, and that contribution is equal in magnitude to the energy density. HINT: Choose 3 orthogonal...
  16. L

    Maxwell Stress Tensor: Find Elements for Plane Wave in Z Direction

    Homework Statement find all elements of maxwell stress tensor for a monochromatic plane wave traveling in z direction and linearly polarized in x. Homework Equations Tij=\epsilono(EiEj-(1/2)\deltaij E2+1/\muo(BiBj-(1/2)\deltaB2 The Attempt at a Solution So i found what E and B is well not...
  17. E

    Maxwell stress tensor coordinate system

    Hello, I am trying to understand the Maxwell Stress Tensor. Specifically, I would like to know if it is coordinate-system dependent (and if so, what the expressions are for the stress tensor in cylindrical and spherical coordinates). Griffiths gives the definition of the maxwell stress tensor...
  18. P

    Maxwell stress tensor in electrodynamics

    \hat{N}=\{\vec{E},\vec{D}\}+\{\vec{H},\vec{B}\}-\frac{1}{2}(\vec{D}\cdot\vec{E}+\vec{B}\cdot\vec{H})\hat{1} \hat{1} - unit tensor If I look \{\vec{E},\vec{D}\}. I know that \{\vec{E},\vec{D}\}=\{\vec{D},\vec{E}\}^* But when I can say that \{\vec{E},\vec{D}\}=\{\vec{D},\vec{E}\}? and when...
  19. T

    Maxwell Stress Tensor Homework: Find E & B Field Components

    Homework Statement x and y are nonconducting cylindrical shells. Both cylindrical shells are surrounding long wires that are carrying current. the x shell out of the page and the y shell into the page. x radius has a charge per unit length = to +\lambda y radius has a charge per unit length =...
  20. T

    How Do You Calculate the Maxwell Stress Tensor Between Cylindrical Shells?

    Homework Statement x and y are nonconducting cylindrical shells. Both cylindrical shells are surrounding long wires that are carrying current. the x shell out of the page and the y shell into the page. x radius has a charge per unit length = to +\lambda y radius has a charge per unit length =...
  21. B

    Maxwell Stress Tensor: Explained for Ben

    Would someone please be able to run me through the different components of the Maxwell Stress Tensor equation. T_{ij} = \epsilon_0 \left( E_i E_j - \frac{1}{2} \delta_{ij} E^2 \right) + \frac{1}{\mu_0} \left( B_i B_j - \frac{1}{2} \delta_{ij} E^2 \right) I don't understand some of it and...
  22. T

    Calculating Force on Particle Using Maxwell Stress Tensor

    Consider a particle with charge q in an static, homogeneous electric field. Using the fact that the net force on the particle in the surface integral of the Maxwell Stress Tensor, and assuming the surface is a sphere around this particle: a) Find the net force on the particle (This part I...
  23. P

    The physical meaning of Maxwell stress tensor

    Maxwell stress tensor: T_{ij} = \epsilon_0 \left( E_i E_j - \frac{1}{2} \delta_{ij} E^2 \right) + \frac{1}{\mu_0} \left( B_i B_j - \frac{1}{2} \delta_{ij} E^2 \right) We can interpret T as the force per unit area acting on the surface. But what surprises me is, T_{ij} = T_{ji}, i.e. the...
  24. G

    Maxwell Stress Tensor: Solutions for Polarized Waves & Coulomb's Law

    URGENT! Hi, I have a couple of urgent problems which are listed below. I am not sure what to do in either of them! If someone could help me as soon as possible that would be great! Cheers Problems: 1. Consider a linearly polarised plane wave incident normally on a slab of material...
  25. M

    Deriving the Maxwell Stress Tensor for a Spherical Charge Distribution

    Consider a spherical volume of radius R filled with a uniform electric charge density p(rowe) a) Use Gauss' law to calculate the electric field E in the interior of the spherical charge b) Use the expression for the electric field to derive an expression for the Maxwell stress tensor...