Right-hand rule

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Right-hand rule

:For the related yet different principle relating to electromagnetic coils, see right hand grip rule
Right hand grip rule

The right hand grip rule is a physics principle applied to electric current passing through a solenoid, resulting in a magnetic field. When you wrap your right hand around the solenoid with your fingers in the direction of the conventional current, your thumb points in the direction of the magnetic north pole....
. In mathematics
Mathematics

Mathematics is the study of quantity, structure, space, change, and related topics of pattern and form. Mathematicians seek out patterns whether found in numbers, space, natural science, computers, imaginary abstractions, or elsewhere....
and physics
Physics

Physics is the natural science which examines basic concepts such as energy, force, and spacetime and all that derives from these, such as mass, charge, matter and its Motion ....
, the right-hand rule is a common mnemonic
Mnemonic

A mnemonic device 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 something, particularly lists, but may be visual, kinesthetic or auditory....
for understanding notation conventions for vectors in 3 dimensions.

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:For the related yet different principle relating to electromagnetic coils, see right hand grip rule
Right hand grip rule

The right hand grip rule is a physics principle applied to electric current passing through a solenoid, resulting in a magnetic field. When you wrap your right hand around the solenoid with your fingers in the direction of the conventional current, your thumb points in the direction of the magnetic north pole....
. In mathematics
Mathematics

Mathematics is the study of quantity, structure, space, change, and related topics of pattern and form. Mathematicians seek out patterns whether found in numbers, space, natural science, computers, imaginary abstractions, or elsewhere....
and physics
Physics

Physics is the natural science which examines basic concepts such as energy, force, and spacetime and all that derives from these, such as mass, charge, matter and its Motion ....
, the right-hand rule is a common mnemonic
Mnemonic

A mnemonic device 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 something, particularly lists, but may be visual, kinesthetic or auditory....
for understanding notation conventions for vectors in 3 dimensions. It was invented for use in electromagnetism by British physicist Zachariah William Cole in the late 1800s.

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.

There are variations on the mnemonic depending on context, but all variations are related to the one idea of choosing a convention.

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
Cross product

In mathematics, the cross product is a binary operation on two vector s in a three-dimensional Euclidean space that results in another vector which is orthogonal to the plane containing the two input vectors....
. The right-hand rule imposes the following procedure for choosing one of the two directions.

With the thumb, index, and middle fingers at right angles to each other (with the index finger pointed straight), the middle finger points in the direction of c when the thumb represents a and the index finger represents b.

Other (equivalent) finger assignments are possible. For example, the first (index) finger can represent a, the first vector in the product; the second (middle) finger, b, the second vector; and the thumb, c, the product.

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
Rotation

A rotation is a movement of an object in a circular motion. A two-dimensional object rotates around a center of rotation. A Three-dimensional space object rotates around a line called an axis....
of a body, a magnetic field or a fluid. 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
Cross product

In mathematics, the cross product is a binary operation on two vector s in a three-dimensional Euclidean space that results in another vector which is orthogonal to the plane containing the two input vectors....
of two vectors. This leads to widespread use in physics
Physics

Physics is the natural science which examines basic concepts such as energy, force, and spacetime and all that derives from these, such as mass, charge, matter and its Motion ....
, 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 only indirectly to cross product
Cross product

In mathematics, the cross product is a binary operation on two vector s in a three-dimensional Euclidean space that results in another vector which is orthogonal to the plane containing the two input vectors....
s, and use the second form.)

The angular velocity
Angular velocity

In physics, the angular velocity is a vector quantity which specifies the angular speed, and axis about which an object is rotating. The SI unit of angular velocity is radians per second, although it may be measured in other units such as degrees per second, revolutions per second, degrees per hour, etc....
of a rotating object and the rotational velocity of any point on the object
A torque
Torque

Torque is the tendency of a force to rotate an object about an axis . Just as a force is a push or a pull, a torque can be thought of as a twist....
, the force that causes it, and the position of the point of application of the force
A magnetic field
Magnetic field

A magnetism field is a vector field which can exert a magnetic force on moving electric charges and on magnetic dipoles . When placed in a magnetic field, magnetic dipoles tend to align their axes parallel to the magnetic field....
, the position of the point where it is determined, and the electric current
Electric current

Electric current is the flow of electric charge. The electric charge may be either electrons or ions.The International System of Units unit of electric current intensity is the ampere....
(or change in electric flux
Electric flux

In electromagnetism, electric flux is the flux of the electric field. Electric flux is proportional to the number of electric field lines going through a virtual surface....
) that causes it
A magnetic field
Magnetic field

A magnetism field is a vector field which can exert a magnetic force on moving electric charges and on magnetic dipoles . When placed in a magnetic field, magnetic dipoles tend to align their axes parallel to the magnetic field....
in a coil of wire and the electric current
Electric current

Electric current is the flow of electric charge. The electric charge may be either electrons or ions.The International System of Units unit of electric current intensity is the ampere....
in the wire
The force of a magnetic field
Magnetic field

A magnetism field is a vector field which can exert a magnetic force on moving electric charges and on magnetic dipoles . When placed in a magnetic field, magnetic dipoles tend to align their axes parallel to the magnetic field....
on a charged particle, the magnetic field itself, and the velocity
Velocity

In physics, velocity is defined as the Derivative of Position vector. It is a vector physical quantity; both speed and direction are required to define it....
of the object
The vorticity
Vorticity

Vorticity is a mathematical concept used in fluid dynamics. It can be related to the amount of "Circulation " or "rotation" in a fluid.The average vorticity in a small region of fluid flow is equal to the Circulation around the boundary of the small region, divided by the area A of the small region....
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 right hand rule

Fleming's right hand rule shows the direction of induced current flow when a Electrical conductor moves in a magnetic field.The right hand is held with the thumb, first finger and second finger mutually at right angles, as shown in the diagram ....
)

Fleming's left hand rule
Fleming's left hand rule

Fleming's left hand rule shows the direction of the thrust on a Electrical conductor carrying a Electric current in a magnetic field.The left hand is held with the thumb, index finger and middle finger mutually at right angles....
is a rule for finding the direction of the thrust
Thrust

Thrust is a reaction force described quantitatively by Isaac Newton's Newton's laws of motion. When a system expels or acceleration mass in one direction the accelerated mass will cause a proportional but opposite force on that system....
on a conductor carrying a current in a magnetic field.

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 material
Left-handed material

Left-handed materials are materials that have simultaneously negative permittivity and negative Permeability . Sometimes, these materials are also designated by the terms doubly negative material or negative index material....
s. Normally, for an electromagnetic wave, the electric and magnetic fields, and the direction of propagation
Wave propagation

Wave propagation is any of the ways in which wave s travel.With respect to the direction of the oscillation relative to the propagation direction, we can distinguish between longitudinal wave and transverse waves....
of the wave obey the right-hand rule. However, left-handed materials have special properties - the negative refractive index. 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
Lorentz force

In physics, the Hendrik Lorentz force is the force on a point charge due to electromagnetic fields. It is given by the following equation in terms of the electric field and magnetic fields:...
), B (direction of the magnetic field) and I (current). 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

External links

National High Magnetic Field Laboratory