# 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.

## Ampere's right hand screw rules

Prediction of direction of field (B), given that the current I flows in the direction of the thumb

### 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 define a 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, for whom the rule was named, was inspired by Hans Christian Oersted, another physicist who experimented with magnet needles. Oersted observed that the needles swirled when in the proximity of an electric current carrying wire, leading to him to the conclusion that electricity could create magnetic fields.

### Application

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

1. An electric current passes through a solenoid, resulting in a magnetic field. When wrapping the right hand around the solenoid with the fingers in the direction of the conventional current, the thumb points in the direction of the magnetic north pole.
2. 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. When gripping the imaginary axis of rotation of the rotational force so that your fingers point in the direction of the force, the extended thumb points in the direction of the torque vector.

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. The thumb points direction of current and fingers point direction of magnetic lines of force.

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

### Introduction

John Ambrose Fleming 1890

You can see a scenario of an electrical wire "cutting" magnetic field lines. "Cutting" refers to the fact that the wire is moving perpendicularly or with an angle to the perpendicular plane of a magnetic field, and is termed "flux cutting". As a result, a current will be induced 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:

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

## 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:

$\mathbf{F} = q\mathbf{v} \times \mathbf{B}$

### 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,

1. Point your index finger in the direction of the first vector A.
2. Point your middle finger in the direction of the second vector B.
3. 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.)

The left-handed orientation is shown on the left, and the right-handed on the right.

## 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