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Right-hand rule
- The right hand rule is also an algorithm used to solve Mazes
In mathematics and physics, the right-hand rule is a convention for determining relative directions of certain vectors.
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Definition
In fact, there are two closely related right-hand rules. The first of these occurs in situations in which a non-commutative operation must be performed on two directions a and b (in a three-dimensional space) that constructs a direction c perpendicular to both a and b. There are in fact two such directions. The right-hand rule imposes the following procedure for choosing one of the two directions.
First, the hand is held flat and positioned so that the fingers are aligned with a. Then, the hand is rotated about the forearm so that the fingers curl inward toward b. The thumb indicates c.
(There is also an alternative technique. First, the forefinger of the right hand is pointed directly forward, and the entire hand positioned so that the forefinger is aligned with a. Then, the middle finger is turned inward (toward the palm), and the hand is turned about the axis defined by a so that the middle finger aligns with b. The thumb indicates c.)
The other form of the right-hand rule occurs in situations where a direction c must be determined based on a rotational direction a, or vice versa. In this case, the fingers of the right hand are curled in the direction of a, and the thumb indicates c.
Applications of the right-hand rule
Perhaps the most fundamental application of the right-hand rule is the Cartesian coordinate system, where the first form is used to position the z-axis once the x- and y-axes have been determined.
The first form of the rule is also used to determine the direction of the cross product of two vectors. This leads to widespread use in physics, wherever the cross product occurs. A list of physical quantities whose directions are related by the right-hand rule is given below. (Some of these are related to cross products only indirectly, and use the second form.)
- The angular velocity of a rotating object and the rotational velocity of any point on the object
- A torque, the force that causes it, and the position of the point of application of the force
- A magnetic field, the position of the point where it is determined, and the electric current (or change in electric flux) that causes it
- A magnetic field in a coil of wire and the electric current in the wire
- The force of a magnetic field on an object, the magnetic field itself, and the velocity of the object
Left-hand rule
Left-handed materials are metamaterials which have a negative refractive index.
The term "left-handed material" was coined by a prediction of Russian theorist V. G. Veselago in 1968.
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