Magnetic field: Difference between revisions

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In [[physics]], a '''magnetic field''' (commonly denoted by '''H''') is a magnetic force (a vector) defined for  every point in space.  
In [[physics]], a '''magnetic field''' (commonly denoted by '''H''') is a magnetic force (a vector) defined for  every point in space; it is a [[vector field]].  


In non-relativistic physics, space is the three-dimensional [[Euclidean space]] <math>\scriptstyle \mathbb{E}^3</math>&mdash;the infinite (Newtonian) world that we live in.  The vector field '''H''' may be pictured as a set of arrows, one arrow for each point of space. In this picture an arrow represent a magnetic force. As for any  vector, the magnetic force is defined by its length (the ''strength'' of the magnetic field) and by its direction.  
In non-relativistic physics, space is the three-dimensional [[Euclidean space]] <math>\scriptstyle \mathbb{E}^3</math>&mdash;the infinite (Newtonian) world that we live in.  The vector field '''H''' may be pictured as a set of arrows, one arrow for each point of space. In this picture an arrow represent a magnetic force. As for any  vector, the magnetic force is defined by its length (the ''strength'' of the magnetic field) and by its direction.  
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The dimension of the magnetic field is [[ampere]]/meter (SI units) or [[oersted]] (Gaussian units);
The dimension of the magnetic field is [[ampere]]/meter (SI units) or [[oersted]] (Gaussian units);
one oersted equals 1000/4π A/m.
one oersted equals 1000/4π A/m.
==Mathematical description==
The magnetic field '''H''' is in general a function of position.  When we choose a [[Cartesian coordinate]] system for <math>\scriptstyle \mathbb{E}^3</math>, a point ''P'' has coordinates ''x'', ''y'' and ''z'', and '''H''' is a vector function '''H'''(''x'',''y'',''z''),
i.e.,
:<math>
\mathbf{H}(x,y,z) = \Big( H_x(x,y,z), H_y(x,y,z), H_z(x,y,z) \Big)\; \hbox{and}\; |\mathbf{H}(x,y,z)| \equiv \sqrt{H^2_x+H^2_y+H^2_z},
</math>
where |'''H'''(''x'',''y'',''z'')| is the strength (also known as intensity) of the field at (''x'',''y'',''z'').  If the vector '''H''' does not depend on position, the field is homogeneous.


Indicating unit vectors along the Cartesian coordinate axes by '''e'''<sub>x</sub>, '''e'''<sub>y</sub>, '''e'''<sub>z</sub>, and the origin of coordinate system by ''O'', we may equivalently write
In modern texts on electricity and magnetism, the vector '''H''' is seen as the magnetic analogue of the [[electric displacement]] '''D'''. In older texts, in which one introduces Coulomb's law for magnetic poles, one finds the emphasis on the analogy of '''H''' and the [[electric field]] '''E'''.
:<math>
\overrightarrow{OP}\equiv \mathbf{r} = \mathbf{e}_x x + \mathbf{e}_y y + \mathbf{e}_z z
\quad\mathrm{and}\quad
\mathbf{H} = \mathbf{e}_x H_x(x,y,z) + \mathbf{e}_y H_y(x,y,z) + \mathbf{e}_z H_z(x,y,z).
</math>
This notation makes clear how rotation of the coordinate system affects '''r''' and '''H''', and  in particular it shows that both vectors obey the same rotation rule.

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In physics, a magnetic field (commonly denoted by H) is a magnetic force (a vector) defined for every point in space; it is a vector field.

In non-relativistic physics, space is the three-dimensional Euclidean space —the infinite (Newtonian) world that we live in. The vector field H may be pictured as a set of arrows, one arrow for each point of space. In this picture an arrow represent a magnetic force. As for any vector, the magnetic force is defined by its length (the strength of the magnetic field) and by its direction.

A magnetic field is called homogeneous if all vectors are parallel and of the same length. If the vectors vary from point to point in length or direction, the field is called non-homogeneous.

The vectors may be time-dependent, i.e., the length and direction of the vectors may change as a function of time; in that case H is said to be a time-dependent field.

The physical source of the magnetic force is the presence of one or more permanent magnets, one or more electric currents (see Biot-Savart's law), or time-dependent electric fields (displacement currents). In general the strength of the magnetic field decreases as a simple function of 1/R, the inverse of the distance R of the field point to the source.

The dimension of the magnetic field is ampere/meter (SI units) or oersted (Gaussian units); one oersted equals 1000/4π A/m.

In modern texts on electricity and magnetism, the vector H is seen as the magnetic analogue of the electric displacement D. In older texts, in which one introduces Coulomb's law for magnetic poles, one finds the emphasis on the analogy of H and the electric field E.

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