## Magnetic moment – simple english wikipedia, the free encyclopedia electricity 3 phase vs single phase

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Physicists represent sources of magnetic moments in materials as poles. The North and South poles are an analogy to the positive and negative charges in electrostatics. Consider a bar magnet which has magnetic poles of equal magnitude but opposite polarity. Each pole is the source of magnetic force which weakens with distance. Since magnetic poles always come in pairs, their forces partially cancel each other because while one pole pulls, the other repels. This cancellation is greatest when the poles are close to each other i.e. when the bar magnet is short. The magnetic force produced by a bar magnet, at a given point in space, therefore depends on two factors: on both the strength p {\displaystyle p} of its poles, and on the vector l {\displaystyle \mathbf {l} } separating them. The moment is defined as [1] m = p l . {\displaystyle \mathbf {m} =p\mathbf {l} .}

It points in the direction from South to North pole. The analogy with electric dipoles should not be taken too far because magnetic dipoles are associated with angular momentum (see Magnetic moment and angular momentum). Nevertheless, magnetic poles are very useful for magnetostatic calculations, particularly in applications to ferromagnets. [1] Practitioners using the magnetic pole approach generally represent the magnetic field by the irrotational field H {\displaystyle \mathbf {H} } , in analogy to the electric field E {\displaystyle \mathbf {E} } . Current loop definition [ change | change source ]

Suppose a planar closed loop carries an electric current I {\displaystyle I} and has vector area S {\displaystyle \mathbf {S} } ( x {\displaystyle x} , y {\displaystyle y} , and z {\displaystyle z} coordinates of this vector are the areas of projections of the loop onto the y z {\displaystyle yz} , z x {\displaystyle zx} , and x y {\displaystyle xy} planes). Its magnetic moment m {\displaystyle \mathbf {m} } , vector, is defined as: m = I S . {\displaystyle \mathbf {m} =I\mathbf {S} .}

By convention, the direction of the vector area is given by the right hand grip rule (curling the fingers of one’s right hand in the direction of the current around the loop, when the palm of the hand is "touching" the loop’s outer edge, and the straight thumb indicates the direction of the vector area and thus of the magnetic moment). [2]

In the most general case of an arbitrary current distribution in space, the magnetic moment of such a distribution can be found from the following equation: m = 1 2 ∫ r × J d V , {\displaystyle \mathbf {m} ={\frac {1}{2}}\int \mathbf {r} \times \mathbf {J} \,{\rm {d}}V,}

Practitioners using the current loop model generally represent the magnetic field by the solenoidal field B {\displaystyle \mathbf {B} } , analogous to the electrostatic field D {\displaystyle \mathbf {D} } . Magnetic moment of a solenoid [ change | change source ]

A generalization of the above current loop is a multi-turn coil, or solenoid. Its moment is the vector sum of the moments of individual turns. If the solenoid has N {\displaystyle N} identical turns (single-layer winding), m = N I S . {\displaystyle \mathbf {m} =NI\mathbf {S} .} Units [ change | change source ]

The unit for magnetic moment is not a base unit in the International System of Units (SI) and it can be represented in more than one way. For example, in the current loop definition, the area is measured in square meters and I {\displaystyle I} is measured in amperes, so the magnetic moment is measured in ampere–square meters ( A m 2 {\displaystyle {\text{A m}}^{2}} ). In the equation for torque on a moment, the torque is measured in Newton.meters and the magnetic field in tesla, so the moment is measured in N.m per Tesla ( N.m T − 1 {\displaystyle {\text{N.m T}}^{-1}} ). These two representations are equivalent: A m 2 = N.m T − 1 . {\displaystyle \,{\text{A m}}^{2}=\,{\text{N.m T}}^{-1}.}

In the CGS system, there are several different sets of electromagnetism units, of which the main ones are ESU, Gaussian, and EMU. Among these, there are two alternative (non-equivalent) units of magnetic dipole moment in CGS: (ESU CGS) 1 statA·cm² = 3.33564095×10 -14 ( m 2· A or N.m/ T)

All formulas in this article are correct in SI units, but in other unit systems, the formulas may need to be changed. For example, in SI units, a loop of current with current I and area A has magnetic moment I×A (see below), but in Gaussian units the magnetic moment is I×A/ c. Intrinsic magnetic moments and spins of some elementary particles [3] Particle