Talk:Maxwell stress tensor

As a maths graduate (many years ago) who skipped the courses that would have taught me this, but did a fair bit of mathematical analysis - a request:

If my inference is correct, then can a small note, or else a link, please be inserted to make plain the notation that
 * $$ E^2=\mathbf{E}\cdot \mathbf{E}$$

-in other words that the unbold, unsubscripted E is just the norm of the bold E vector? And similarly for B. Else, if I have this wrong, then can words be inserted that would prevent me from making this assumption.

Thanks. — Preceding unsigned comment added by 83.217.170.175 (talk) 14:51, 30 July 2012 (UTC)


 * $$|\mathbf{V}|^2 = \mathbf{V} \cdot \mathbf{V} = V^2 $$ for any vector $$\mathbf{V}$$ in $$\mathbb{R}^3$$, it is just a notation to drop the bold font, or the arrow, meaning the norm of the vector. Heitorpb (talk) 09:10, 12 October 2015 (UTC)

Cylindrical Objects
The article currently says: "For cylindrical objects, such as the rotor of a motor, this is further simplified to: :$$\sigma_{r t} = \frac{1}{\mu_0} B_r B_t - \frac{1}{2 \mu_0} B^2 \delta_{r t} \,.$$"

Wouldn't it be clearer to simply say :$$\sigma_{r t} = \frac{1}{\mu_0} B_r B_t \,.$$? After all, the Kroenecker delta is zero, because r is not t. I've been staring at this equation wondering why anyone would want to leave that term in the expression. I will wait a while to see if there are any objections, and then change it.--JB Gnome (talk) 02:06, 2 February 2014 (UTC)

Lorentz force vs. Maxwell stress tensor
If one had a positive point charge at r=0 surrounded by a negatively-charged spherical shell at r=1 with equal, but opposite charge, then clearly there would be an electric field extending from r=0 to r=1. Also, an electric field of a positive charge positioned just outside the spherical shell at r=1+ε (ε>0) would have an electric field extending to infinity, and this field would clearly overlap the field interior of the spherical shell. The Lorentz force computation considered by the net E-field from the sphere at r=1+ε and the charge positioned at r=1+ε returns zero force, and yet, the energy computation (or the Maxwell stress tensor rather) does not return a zero result and predicts a force. I'm not the only one who is concerned about a similar problem. See Advances in Applied Science Research, 2011, 2 (2): 99-102 for an example of two positron fields whose fields are limited to some radius r from the respective centers of each:

http://connection.ebscohost.com/c/articles/64287573/nuclear-force-electrostatics

"The nuclear force in electrostatics AUTHOR(S) Singer, Michael

PUB. DATE April 2011

SOURCE Advances in Applied Science Research;Apr2011, Vol. 2 Issue 2, p99

SOURCE TYPE Academic Journal

DOC. TYPE Article

ABSTRACT This paper proposes an electrostatic model for the nuclear force. This uses a simple bounded electrostatic field to create the composite attractive and repulsive forces seen when two nucleons are in very close proximity. Rather than attempt to model such a force using the gross behaviour of electrons or positrons, whose electric fields extend to infinity, it works from first principles and applies finite element analysis first to the positron to demonstrate that the seeds of nucleonnucleon interaction have their roots in the positron-positron interaction, and then truncates the positron field at a fixed radius and shows that nucleonic attraction-repulsion results. ACCESSION # 64287573"

A copy of the article can be found at Pelagia Research Library (http://pelagiaresearchlibrary.com/advances-in-applied-science/vol2-iss2/AdASR-2011-2-2-99-102.pdf).siNkarma86—Expert Sectioneer of Wikipedia undefined 14:21, 31 July 2013 (UTC)


 * I don't think the electric field won't be equal to zero unless all the charges on and within the sphere aren't allowed to move. Like, on a conductor surface charges can also move and polarize. If they can't move, then they all tug and push on the outside charge so then there's zero Lorentz force and E field. Coulomb's Law is a special case of the Jefimenko equations. In the general case where charge distributions can move, along with the Coulomb q/r^2, you also get a (dq/dt)/(rc) term and a (dJ/dt)/(rc^2) term. 2600:1702:3C50:74A0:6D74:219:A7A3:EB73 (talk) 21:38, 26 September 2023 (UTC)