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.
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?
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)##...
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...
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...
<< 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}##...
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...
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...
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 \...
(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.
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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...
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
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} =...
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?
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...
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...
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...
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...
\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...
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 =...
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 =...
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...
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...
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...
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...
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...