Magnetic+Hand+Rule

=Magnetic Hand Rule= include page="foo"

It is often difficult for students to understand the conventions of vector notation in three dimensions, and thus it may become necessary to employ a mnemonic device. Traditionally, many physics students have relied on **hand rules** for understanding the three-dimensional vectors of magnetic forces, although there are various other methods which do not involve using one's hands. It is useful to memorize and utilize the mnemonic which is most convenient for the user.

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Magnetic Force On a Particle Moving In a Magnetic Field
In magnetics, the direction of a magnetic force vector **F** on a particle moving at velocity **v** through a magnetic field **B** is perpendicular to the vectors of the magnetic field and the velocity. It is easy to determine the direction of magnetic force vectors, given the direction of the other two vectors, by using any of the following mnemonics.

Hand Rule
This rule involves having the palm flat and pointing the thumb ninety degrees outward, as if one is about to give a handshake. The //thumb// must point in the direction of the //velocity// of the particle, and the //other four fingers// must point in the direction of the //magnetic field// in which the particle is located. The direction of the //magnetic force// vector will be //perpendicular to the surface of the palm// after these other conditions are met.

If the particle moving through the magnetic field is a proton, then one must apply these steps using their right hand. If the particle is an electron, these steps apply only if the left hand is used instead. Useful mnemonics for remembering these conditions is that "it is **right** to be **positive**," or "e**left**rons use the **left**."

There are several variations on the hand rule that are also taught by physics teachers, and which are all equally as valid and useful mnemonics. In one popular variation, the index finger points in the direction of the velocity, the middle finger points in the direction of the magnetic field at a right angle to the index finger, and the thumb, perpendicular to both vectors, points in the direction of the magnetic force.

One disadvantage to this rule is that it potentially involves the user to orient their hand in awkward, uncomfortable positions in order to find the magnetic force vector. Otherwise, this rule is very convenient in that it can be used virtually anywhere as long as the user has at least one hand. [//Figure// ]

Book Rule
The book rule is an alternative to the hand rule which requires having a book nearby. The //front cover// points in the direction of the //velocity//, the //back cover// points in the direction of the //magnetic field//, and the //magnetic force// runs //along the spine out the top of the book//.


 * This setup is primarily for positively-charged particles by default**, although it is not difficult to adapt it for negatively-charged particles; **if the particle is negatively-charged**, one must simply remember that **the magnetic force instead runs along the spine out the bottom of the book.**

This method is useful in that it utilizes equipment that is readily available wherever there is studying, whether it be in libraries, coffee shops, or even at home. [//Figure// ]

Guitar rule
The guitar rule is yet another alternative which may be easier imagined rather than using an actual guitar, unless the user is one who is apt to carry around guitars or ukuleles on campus. It is useful for guitarists and ukulele players. The //direction the user strums// is the direction of the //velocity//, and the //neck// of the instrument points in the direction of the //magnetic field//. The __sound__ is emitted outward in the direction of the //magnetic force//.


 * The way the user strums is important.** If the particle is positive, the user must strum downward; if the particle is negative, the user must strum upward. This may be potentially confusing unless one considers that normally, guitar players strum downward first, and usually physics professors refer to positively-charged particles.

Magnetic Field of a Long, Straight Wire
In magnetics, when a current **I** is run through a long, straight wire, a magnetic field **B** is generated that circles around the wire. When talking about current flow, the conventional current flow which involves the transfer of positive charge is usually referred to.

Grip Rule
The user wraps their hand on the wire with the __thumb pointing__ in the direction of the __current__, and then the __other fingers will curl__ in the direction of the __magnetic field__.

When using this mnemonic, one must be aware that when **I** refers to conventional current flow, the right hand must be used; when it refers to the flow of electrons in the wire, the left hand must be used. The mnemonic for the conditions of the magnetic force hand rule may be used for the magnetic field of the straight wire hand rule ("it is **right** to be **positive**," or "e**left**rons use the **left** hand"). [//Figure// ]

This mnemonic may also be used to determine the magnetic field around a loop of wire. The rule is used in this situation the same way it is used in the case of a straight wire, including its conditions. The thumb points in the direction of the current, while the other fingers curl one way or another into the loop to reveal the direction of the magnetic field.

[//Figure// ]

Examples
//An electron is moving towards a magnetic field pointed inward. What will be the initial direction of the magnetic force acting on the electron as it enters the field?//

The particle is an electron, so we must use our left hand. The velocity is downward, so we must point our left thumb downward. The magnetic field is directed into the page, so the remaining fingers must correspond. When you direct your thumb downwards and your other fingers toward the page, palm faces left. Thus, the vector of the initial magnetic force acting on the particle is directed **left**.