# Right-hand rule

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In mathematics and physics, the **right-hand rule** is a common mnemonic for understanding notation conventions for vectors in 3 dimensions. There are several right hand rules that make it easy to understand the invisible matters or substances.

## Ampère's right hand screw rules

### Introduction

Ampère's right hand screw rule (also called *right-hand grip rule*, *coffee-mug rule*, or the *corkscrew-rule*), is used either when a vector (such as the Euler vector) must be defined to represent the rotation of a body, a magnetic field or a fluid, or vice versa when it is necessary to decode the rotation vector, to understand how the corresponding rotation occurs. It reveals a connection between the current and the magnetic field lines in the magnetic field that the current created.
André-Marie Ampère, a French physicist and mathematician, who discovered this rule, inspired by Hans Christian Oersted, another physicist who did an experiment of a magnet needle swirled when an electric current went by, meaning electricity could create magnetic field. After that, Ampere was encouraged to explain the phenomenon by using physical and mathematical ways. Then the easy-doing rule was discovered.

### Application

This version of the rule is used in two complementary applications of Ampère's circuital law:

- An electric current passes 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.
- An electric current passes through a straight wire. Here, the thumb points in the direction of the conventional current (from positive to negative), and the fingers point in the direction of the magnetic lines of flux.

The rule is also used to determine the direction of the torque vector. If you grip the imaginary axis of rotation of the rotational force so that your fingers point in the direction of the force, then the extended thumb points in the direction of the torque vector.

The right-hand rule is just a convention. When applying the rule to current in a straight wire, for example, the direction of the magnetic field (counterclockwise instead of clockwise when viewed from the tip of the thumb) is a result of this convention and not an underlying physical phenomenon.

## Right hand rules for electrical wire "cutting" magnetic field lines

### Introduction

You can see a scenario of an electrical wire "cutting" magnetic field lines. The word cutting means that the wire is moving perpendicularly or with an angle to the perpendicular plane of a magnetic field. As a result, it will appear currents inside the electric wire. The right-hand rule is used to identify the direction of the current. John Ambrose Fleming, an English engineer and physicist, discovered the rule.

As the picture illustrated, the steps of the right-hand rule is showed below:

- Identify the direction of how the magnetic field lines goes and palm up. Imagine the lines can go through your palm.
- Then, point the cutting direction of the wire with your thumb, which should be perpendicular to the other four fingers.
- The direction of the other four fingers is the which of the current.

## Right-hand rule for cross products

The cross product of two vectors is often encountered in physics and engineering. For example, in statics and dynamics, torque is the cross product of lever length and force, and angular momentum is the cross product of linear momentum and distance from an origin. In electricity and magnetism, the force exerted on a moving charged particle when moving in a magnetic field B is given by:

### Magnetic force on a moving charged particle

The direction of the cross product may be found by application of the right hand rule as follows: Using your right hand,

- Point your index finger in the direction of the first vector A.
- Point your middle finger in the direction of the second vector B.
- Your thumb will point in the direction of the cross product C.

For example, for a positively charged particle moving to the North, in a region where the magnetic field points West, the resultant force will point up.^{[1]}

## Applications

The first form of the rule is 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 only indirectly to cross products, and use the second form.)

- For a rotating object, if the right-hand fingers follow the curve of a point on the object, then the thumb points along the axis of rotation in the direction of the angular velocity vector
- 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 a charged particle, 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)
- The x, y and z unit vectors in a Cartesian coordinate system can be chosen to follow the right-hand rule. Right-handed coordinate systems are often used in rigid body physics and kinematics.

## Coordinate orientation

Axis or vector | Right-hand | Right-hand (alternative) |
---|---|---|

X, 1, or A | First or index | Thumb |

Y, 2, or B | Second finger or palm | First or index |

Z, 3, or C | Thumb | Second finger or palm |

^{[2]}
^{[3]}

## See also

- Chirality (mathematics)
- Curl (mathematics)
- Fleming's left-hand rule for motors
- Improper rotation
- ISO 2
- Pseudovector
- Reflection (mathematics)
- Vorticity

## References

## 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
- Weisstein, Eric W., "Right-hand rule",
*MathWorld*. - Dr. Johannes Heidenhain : Right Hand Rule - Heidenhain TNC Training : heidenhain.de
- Christian Moser : right-hand-rule : wpftutorial.net