- For the related yet different principle relating to electromagnetic coils, see right hand grip rule. For the related yet different principle relating to electromagnetic coils see Right-hand rule.
In mathematics and physics, the right-hand rule is a common mnemonic for understanding notation conventions for vectors in 3 dimensions. Mathematics is the body of Knowledge and Academic discipline that studies such concepts as Quantity, Structure, Space and Physics (Greek Physis - φύσις in everyday terms is the Science of Matter and its motion. A mnemonic device (nəˈmɒnɪk is a Memory aid Commonly met mnemonics are often verbal something such as a very short poem or a special word used to help a person remember It was invented by British physicist Ambrose Fleming in the early 1900s[1]
When choosing three vectors that must be at right angles to each other, there are two distinct solutions, so when expressing this idea in mathematics, one must remove the ambiguity of which solution is meant. Sir John Ambrose Fleming ( November 29, 1849 - April 18, 1945) was an English Electrical engineer and Physicist
There are variations on the mnemonic depending on context, but all variations are related to the one idea of choosing a convention.
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Direction associated with an ordered pair of directions
One form of the right-hand rule is used in situations in which an ordered operation must be performed on two vectors a and b that has a result which is a vector c perpendicular to both a and b. The most common example is the vector cross product. In Mathematics, the cross product is a Binary operation on two vectors in a three-dimensional Euclidean space that results in another vector which The right-hand rule imposes the following procedure for choosing one of the two directions.
- Hold the thumb, index and middle fingers at right angles to each other. Make sure that the thumb and index finger form an "L" or a gun shape. The middle finger is the direction of c when the thumb represents a and the index finger represents b.
Direction associated with a rotation
A different form of the right-hand rule is used in situations where a vector must be assigned to the rotation of a body, a magnetic field or a fluid. A rotation is a movement of an object in a circular motion A two- Dimensional object rotates around a center (or point) of rotation Alternatively, when a rotation is specified by a vector, and it is necessary to understand the way in which the rotation occurs, the right-hand rule is applicable.
In this form, the fingers of the right hand are curled to match the curvature and direction of the motion or the magnetic field. The thumb indicates the direction of the vector.
Applications
The first form of the rule is used to determine the direction of the cross product of two vectors. In Mathematics, the cross product is a Binary operation on two vectors in a three-dimensional Euclidean space that results in another vector which This leads to widespread use in physics, wherever the cross product occurs. Physics (Greek Physis - φύσις in everyday terms is the Science of Matter and its motion. A list of physical quantities whose directions are related by the right-hand rule is given below. (Some of these are related only indirectly to cross products, and use the second form. In Mathematics, the cross product is a Binary operation on two vectors in a three-dimensional Euclidean space that results in another vector which )
- 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
- The vorticity at any point in the field of flow of a fluid
- The induced current from motion in a magnetic field (known as Fleming's right hand rule)
Fleming's left hand rule is a rule for finding the direction of the thrust on a conductor carrying a current in a magnetic field. Do not confuse with Angular frequency The unit for angular velocity is rad/s Rotational speed (sometimes called speed of revolution) indicates for example how fast a motor is running A torque (τ in Physics, also called a moment (of force is a pseudo- vector that measures the tendency of a force to rotate an object about In Physics, a force is whatever can cause an object with Mass to Accelerate. In Physics, a magnetic field is a Vector field that permeates space and which can exert a magnetic force on moving Electric charges Electric current is the flow (movement of Electric charge. The SI unit of electric current is the Ampere. In Electromagnetism, electric flux is Flux of the Electric field. In Physics, a magnetic field is a Vector field that permeates space and which can exert a magnetic force on moving Electric charges Electric current is the flow (movement of Electric charge. The SI unit of electric current is the Ampere. In Physics, a magnetic field is a Vector field that permeates space and which can exert a magnetic force on moving Electric charges In Physics, velocity is defined as the rate of change of Position. Vorticity is a mathematical concept used in Fluid dynamics. It can be related to the amount of " circulation " or "rotation" (or more strictly the Faraday's law of induction describes an important basic law of electromagnetism which is involved in the working of Transformers Inductors and many forms of Fleming's right hand rule (for Generators) shows the direction of Induced current flow when a conductor moves in a Magnetic field. Fleming's left hand rule (for Electric motors shows the direction of the Thrust on a conductor carrying a current in a Magnetic field Thrust is a reaction force described quantitatively by Newton 's Second and Third Laws.
Left handedness
In certain situations, it may be useful to use the opposite convention, where one of the vectors is reversed and so creates a left-handed triad instead of a right-handed triad.
An example of this situation is for left-handed materials. Left-handed materials are materials that have simultaneously negative Permittivity and negative permeability. Normally, for an electromagnetic wave, the electric and magnetic fields, and the direction of propagation of the wave obey the right-hand rule. Electromagnetic radiation takes the form of self-propagating Waves in a Vacuum or in Matter. In Physics, magnetism is one of the Phenomena by which Materials exert attractive or repulsive Forces on other Materials. Wave propagation is any of the ways in which waves travel through a Waveguide. However, left-handed materials have special properties - the negative refractive index. A metamaterial (or meta material) is a material which gains its properties from its structure rather than directly from its composition It makes the direction of propagation point in the opposite direction.
De Graaf's translation of Fleming's left-hand rule - which uses thrust, field and current - and the right-hand rule, is the FBI rule. The FBI rule changes Thrust into F (Lorentz force), B (direction of the magnetic field) and I (current). In Physics, the Lorentz force is the Force on a Point charge due to Electromagnetic fields It is given by the following equation The FBI rule is easily remembered by US citizens because of the commonly known abbreviation for the Federal Bureau of Investigation.
Symmetry
| Vector | Right-Hand | Right-Hand | Right-Hand | Left-Hand | Left-Hand | Left-Hand |
|---|---|---|---|---|---|---|
| a, x or I | Thumb | Fingers or Palm | First or Index | Thumb | Fingers or Palm | First or Index |
| b, y or B | First or Index | Thumb | Fingers or Palm | Fingers or Palm | First or Index | Thumb |
| c, z or F | Fingers or Palm | First or Index | Thumb | First or Index | Thumb | Fingers or Palm |
See also
- Chirality (mathematics)
- Cross product
- Right hand grip rule
- Curl
- Pseudovector
- Improper rotation
- Reflection (mathematics)
- Fleming's left hand rule
- Vorticity
External links
- Right and Left Hand Rules - Interactive Java Tutorial National High Magnetic Field Laboratory
- A demonstration of the right-hand rule at physics.syr.edu
- Definition at mathworld.wolfram.com
- Comic depicting other alternatives to the right-hand rule
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