Right-hand rule

In mathematics and physics, the right-hand rule is a convention and a mnemonic, utilized to define the orientation of axes in three-dimensional space and to determine the direction of the cross product of two vectors, as well as to establish the direction of the force on a current-carrying conductor in a magnetic field.

The various right- and left-hand rules arise from the fact that the three axes of three-dimensional space have two possible orientations.

The right-hand rule dates back to the 19th century when it was implemented as a way for identifying the positive direction of coordinate axes in three dimensions.

William Rowan Hamilton, recognized for his development of quaternions, a mathematical system for representing three-dimensional rotations, is often attributed with the introduction of this convention.

[1] Josiah Willard Gibbs recognized that treating these components separately, as dot and cross product, simplifies vector formalism.

This transition led to the prevalent adoption of the right-hand rule in the contemporary contexts.

[3] The right-hand rule in physics was introduced in the late 19th century by John Fleming in his book Magnets and Electric Currents.

For left-handed coordinates, the above description of the axes is the same, except using the left hand; and the ¼ turn is clockwise.

Reversing two axes amounts to a 180° rotation around the remaining axis, also preserving the handedness.

If the thumb is pointing north, Earth rotates according to the right-hand rule (prograde motion).

This rule is used in two different applications of Ampère's circuital law: The cross product of two vectors is often taken in physics and engineering.

For example, as discussed above, the force exerted on a moving charged particle when moving in a magnetic field B is given by the magnetic term of Lorentz force: The direction of the cross product may be found by application of the right-hand rule as follows: For example, for a positively charged particle moving to the north, in a region where the magnetic field points west, the resultant force points up.

Rather, the definition depends on chiral phenomena in the physical world, for example the culturally transmitted meaning of right and left hands, a majority human population with dominant right hand, or certain phenomena involving the weak force.