# Cross product in Physics [closed]

The most famous cross product in physics is the one linked to Lorenz's force.

In which other models that describe physical interactions is the cross product used? Are there other laws related to the cross product?

Thank you.

## closed as too broad by Emilio Pisanty, Ben51, By Symmetry, ja72, Qmechanic♦Oct 15 at 14:15

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• One example is torque. – Bob D Oct 15 at 11:50
• Do you mean angular momentum conservation? – Ferdinando Vino Oct 15 at 11:56
• No. I was simply referring to torque or moment. The cross product of the radius vector $r$ and the force $F$ from a point to the line of action of the force. Moment is then a vector perpendicular to the plane containing $r$ and $F$. – Bob D Oct 15 at 12:10
• Moment of force $\overrightarrow{L}=\overrightarrow{r}x\overrightarrow{F}$ – baponkar Oct 15 at 12:56

There are many notable examples in electromagnetism. To name just three of them:

• The flow of energy in electromagnetic radiation (usually called the Poynting vector) is proportional to the cross product of the electric and magnetic fields.

• The torque on a current loop in a constant magnetic field is proportional to the cross product of the (oriented) area vector of the loop and the magnetic field vector.

• Two of the four Maxwell's Laws involve taking the curl of a vector field, which is equivalent to taking the cross product between a vector of derivative operators and the vector field.

There's also a fairly notable example in plasma physics, aptly named "$$\mathbf{E}\times\mathbf{B}$$ drift", which is an acceleration on a charged particle that depends on the cross product of the electric and magnetic fields.

I'm not sure why the cross product in the Loren force would be particularly "famous", but another (almost trivial) example, that you probably encountered before the Lorenz force, is of course angular momentum ;)

PS I would have commented this simple answer, but I do not yet have enough reputation to do so!

• This is a property not a low. My question was: is there an interaction low that needs a cross product do be represented in physics? – Ferdinando Vino Oct 15 at 12:00
• I'm sorry, it seems I didn't read your question carefully enough! – AntimatterHedgehog Oct 15 at 12:11