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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. It was invented for use in electromagnetism by British physicist John Ambrose Fleming in the late 19th century.
When choosing three vectors that must be at right angles to each other, there are two distinct solutions. This can be seen by holding your hands together, palm up, with the fingers curled. If the curl of your fingers represents a rotation from the first axis to the second, then the third axis can point either along your right thumb or your left thumb.
There are variations on the mnemonic depending on context, but all variations are related to the one idea of choosing a convention.
Imagine the right handed screw to be held in the place in which particle is performing circular motion. If the right handed screw is rotated in the direction of particle performing circular motion, then the direction in which screw tip of right handed screw advanced, give the direction of angular displacement and velocity.
Let the X and Y axes define a horizontal plane with the X axis pointing towards the right and Y axis pointing away from you. Then the Z axis can either point up (right-handed) or down (left-handed). If the coordinates are right-handed, then you can place your right thumb on the first or X axis of the X-Y plane, let your index finger point to the second or Y axis. This forms a curl, as to the image, which allows the middle finger to point up along the third or Z axis.
If the coordinates were left handed the thumb of your left hand pointing to the X axis and index toward the Y axis, the middle finger would curl down to point along the Z axis.
If X and Y axes define a vertical plane and the coordinates are right-handed, then with the X axis pointing towards the right and Y axis pointing upwards, then the Z axis would point towards you.
If any of the one axes is reversed the handedness changes. To preserve handedness one of the other axes must also reverse which is equivalent to switching the labels on the other two axes. Note that the handedness of coordinates has no meaning unless the axes are labeled in sequence: a,b,c; 1,2,3; or x,y,z.
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. The right-hand rule imposes the following procedure for choosing one of the two directions.
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.
A different form of the right-hand rule, sometimes called the right-hand grip 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.
This version of the rule is used in two complementary applications of Ampère's circuital law:
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.
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.)
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. Normally, for an electromagnetic wave, the electric and magnetic fields, and the direction of propagation of the wave obey the right-hand rule. However, left-handed materials have special properties, notably 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), 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.
|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|
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