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

In summary, the conversation is about creating a list of cross products in physics. The speaker asks for help in increasing their list, and clarifies that they are not including the curl operator. They estimate that there may be at least 50 different cross products in all of physics. It is mentioned that cross products can be used as a computational aid in dealing with physical bodies and can also occur in physical laws. The speaker references a Wikipedia article that provides examples of cross products being used in various applications. The question of whether curl should be included in the list of cross products is raised, with the speaker noting that there are a fair number of occurrences in concepts such as Maxwell's equations and vorticity.
  • #1
faheemahmed6000
18
0
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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  • #2
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
 
  • #3
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.
 
  • #4
Khashishi said:
Are you counting curl as a cross product?
faheemahmed6000 said:
Please not that I am not talking about the curl operator
 

What is a cross product in physics?

A cross product is a mathematical operation that combines two vectors to create a new vector that is perpendicular to both of the original vectors. It is often used in physics to calculate torque, angular momentum, and magnetic fields.

Why is the cross product important in physics?

The cross product is important in physics because it allows us to calculate quantities that are perpendicular to the original vectors, which are essential in many physical phenomena. It also helps us understand the relationship between different vectors and their directions.

What is the formula for calculating a cross product?

The formula for calculating a cross product is A x B = |A| |B| sin(theta) n, where A and B are the two vectors being multiplied, theta is the angle between the two vectors, and n is the unit vector perpendicular to both A and B.

Can you give an example of a cross product in physics?

An example of a cross product in physics is calculating the torque on a spinning wheel. The cross product of the force applied to the wheel and the vector representing the distance from the center of the wheel to where the force is applied gives us the torque acting on the wheel.

Are there any other applications of the cross product in physics?

Yes, the cross product is also used in calculating the direction of the magnetic field generated by a current-carrying wire, determining the direction of angular momentum in a rotating system, and finding the direction of the force acting on a charged particle in a magnetic field.

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