Best straightforward method to calculate the direction of the Lorentz force

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SUMMARY

The discussion centers on the calculation of the direction of the Lorentz force, emphasizing the use of the vector cross product. Participants recommend using the right-hand rule for positive charges and the left-hand rule for negative charges to determine the force's direction. The cross product is illustrated using the standard Cartesian coordinate system, where the cross product of the x-axis and y-axis results in the z-axis. Additionally, a mnemonic involving finger positioning is suggested to aid in remembering the cross product's orientation.

PREREQUISITES
  • Understanding of vector mathematics, specifically vector products.
  • Familiarity with the right-hand and left-hand rules in physics.
  • Basic knowledge of Cartesian coordinates and their representation.
  • Concept of electric charge polarity and its effect on force direction.
NEXT STEPS
  • Study the application of the right-hand rule in electromagnetism.
  • Learn about the mathematical properties of the cross product in vector calculus.
  • Explore the implications of charge polarity on electromagnetic forces.
  • Investigate practical examples of the Lorentz force in physics experiments.
USEFUL FOR

Students of physics, educators teaching electromagnetism, and anyone seeking to understand the principles of the Lorentz force and vector products.

greg_rack
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Hi guys, I'm being introduced to magnetism, and the direction of the Lorentz force is quite confusing since it's involving a vector product.
Which method would you recommend me in order to easily deduce the direction?
 
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Can you write which formula you are having trouble with?
 
greg_rack said:
.. it's involving a vector product.
Which method would you recommend me in order to easily deduce the direction?

Right_hand_rule_cross_product.svg


From: https://en.wikipedia.org/wiki/Cross_product#Definition

But note that for negative charges the direction flips, so you can use the left hand.
 
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greg_rack said:
That's what I meant, thank you very much!
Alternatively, imagine the usual ##x-y## axes, with the x-axis pointing left to right across the page and the y-axis pointing up the page, then the z-axis is upwards from the page. And ##\vec x \times \vec y = \vec z##.
 
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greg_rack said:
That's what I meant, thank you very much!
Note that you can cycle the fingers used. I personally find this easier to remember:

thumb X index-finger = middle-finger

because it is the finger order I use in counting.
 
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