Right-Hand Rule
Short Description of Topic
The Main Idea
The Right-Hand Rule is an easy way to find the direction of a cross product interaction before doing the math.
A Mathematical Model
The Right-Hand Rule is mathamatically modeled by the cross product:
- [math]\displaystyle{ \mathbf{u\times v}=(u_2v_3\mathbf{i}+u_3v_1\mathbf{j}+u_1v_2\mathbf{k}) -(u_3v_2\mathbf{i}+u_1v_3\mathbf{j}+u_2v_1\mathbf{k}) }[/math]
A Computational Model
The cross product is used to describe many magnetic interactions, for example, magnetic field created by a moving charge or a current and magnetic force on a particle by a magnetic field. Because of this, using the right hand rule, to determine the direction of a cross product, can be a useful to check behind the math for sign errors.
Follow the chart bellow to find which fingers correspond to which vectors.
- [math]\displaystyle{ \mathbf{A\times B}=\mathbf{C} }[/math]
| Vector | Right-hand | Right-hand (alternative) |
|---|---|---|
| A | First or index | Thumb |
| B | Second finger or palm | First or index |
| C | Thumb | Second finger or palm |
Examples
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