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

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SUMMARY

This discussion focuses on identifying various cross products in physics, specifically excluding the curl operator. Key examples provided include 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 ($\vec{F_{B}}=\vec{v}\times\vec{B}$), and the Poynting Vector ($\vec{S}=\vec{E}\times\vec{H}$). The discussion suggests that there may be at least 50 different cross products relevant to physics, emphasizing the need for a comprehensive list.

PREREQUISITES
  • Understanding of vector operations in physics
  • Familiarity with fundamental physics concepts such as force, momentum, and electromagnetic fields
  • Knowledge of mathematical notation used in physics, including vector notation and cross product
  • Basic understanding of physical laws like Maxwell's equations
NEXT STEPS
  • Research the applications of cross products in classical mechanics
  • Explore the role of cross products in electromagnetism, particularly in Maxwell's equations
  • Investigate the significance of the Poynting vector in electromagnetic theory
  • Examine the relationship between cross products and angular momentum in rotational dynamics
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Students and professionals in physics, educators teaching vector calculus, and researchers interested in the applications of cross products in various physical laws.

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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