Can anybody give me a list of all cross products in physics.

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Discussion Overview

The discussion centers around identifying and compiling a comprehensive list of cross products used in physics. Participants explore various examples and clarify the scope of what constitutes a cross product, distinguishing between physical laws and computational applications.

Discussion Character

  • Exploratory, Debate/contested

Main Points Raised

  • One participant lists several examples of cross products, including torque, angular momentum, velocity, Biot-Savart law, Lorentz force law, and the Poynting vector.
  • Another participant questions whether the inquiry includes cross products as computational tools or only those found in physical laws.
  • A third participant mentions the curl operator as a potential cross product, referencing its occurrence in Maxwell's equations and vorticity.
  • A later reply reiterates the original request to exclude the curl operator from the discussion.

Areas of Agreement / Disagreement

Participants do not reach a consensus on whether to include the curl operator in the list of cross products, indicating a disagreement on the scope of the inquiry.

Contextual Notes

There are limitations regarding the definitions of cross products and the criteria for inclusion in the list, as well as the potential for numerous examples across different areas of physics.

faheemahmed6000
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Can anybody give me a list of all cross products in physics. I have the following in my list:

Torque
$$\vec{\tau}=\vec{F}\times\vec{r}$$
Angular momentum
$$\vec{L}=\vec{r}\times\vec{p}$$
Velocity
$$\vec{v}=\vec{\omega}\times\vec{r}$$
Biot-Savart law
$$\vec{dB}=\dfrac{\vec{i dl}\times\hat{r}}{r^{2}}$$
Lorentz force law
$$\vec{F_{B}}=\vec{v}\times\vec{B}$$
Poynting vector
$$\vec{S}=\vec{E}\times\vec{H}$$

Can anybody help me in increasing this list as much as possible.

Please not that I am not talking about the curl operator

(My guess is there there may be at least 50 different cross products in all of physics)
 
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Are you counting the cross product as a computational aid in dealing with physical bodies, or are you just interested in occurrences in physical laws? A small list of the former, but enough to get an idea, is presented in https://en.wikipedia.org/wiki/Cross_product#Applications
 
Are you counting curl as a cross product?
##\nabla \times \mathbf{v}##
There's a fair number of those. For example, Maxwell's equations and vorticity.
 
Khashishi said:
Are you counting curl as a cross product?
faheemahmed6000 said:
Please not that I am not talking about the curl operator
 

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