# Talk:Maxwell stress tensor

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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

${\displaystyle E^{2}=\mathbf {E} \cdot \mathbf {E} }$

-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)

${\displaystyle |\mathbf {V} |^{2}=\mathbf {V} \cdot \mathbf {V} =V^{2}}$ for any vector ${\displaystyle \mathbf {V} }$ in ${\displaystyle \mathbb {R} ^{3}}$, 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: :${\displaystyle \sigma _{rt}={\frac {1}{\mu _{0}}}B_{r}B_{t}-{\frac {1}{2\mu _{0}}}B^{2}\delta _{rt}\,.}$"

Wouldn't it be clearer to simply say :${\displaystyle \sigma _{rt}={\frac {1}{\mu _{0}}}B_{r}B_{t}\,.}$? 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