Magnetostatics
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Magnetostatics is the study of magnetic fields in systems where
the currents are steady (not changing with time). It is the magnetic analogue
of electrostatics, where the charges are stationary. The magnetization need not
be static; the equations of magnetostatics can be used to predict
fast magnetic switching events that occur on time scales of nanoseconds or
less. Magnetostatics is even a good approximation when the currents are not
[1]
static – as long as the currents do not alternate rapidly. Magnetostatics is
widely used in applications of micromagnetics such as models of magnetic
storage devices as in computer memory.
Applications[edit]
Magnetostatics as a special case of Maxwell's equations[edit]
Starting from Maxwell's equations and assuming that charges are either fixed
or move as a steady current , the equations separate into two
equations for the electric field (see electrostatics) and two for the magnetic
field. The fields are independent of time and each other. The magnetostatic
[2]
equations, in both differential and integral forms, are shown in the table below.
Form
Name
Differential Integral
Gauss's law
for magnetism
Ampère's law
Where ∇ with the dot denotes divergence, and B is the magnetic flux density,
the first integral is over a surface with oriented surface element
. Where ∇ with the cross denotes curl, J is the current density and H is
the magnetic field intensity, the second integral is a line integral around a
closed loop with line element . The current going through the
loop is .
The quality of this approximation may be guessed by comparing the above
equations with the full version of Maxwell's equations and considering the
importance of the terms that have been removed. Of particular significance is
the comparison of the term against the term. If the
Jump to navigationJump to search
Magnetostatics is the study of magnetic fields in systems where
the currents are steady (not changing with time). It is the magnetic analogue
of electrostatics, where the charges are stationary. The magnetization need not
be static; the equations of magnetostatics can be used to predict
fast magnetic switching events that occur on time scales of nanoseconds or
less. Magnetostatics is even a good approximation when the currents are not
[1]
static – as long as the currents do not alternate rapidly. Magnetostatics is
widely used in applications of micromagnetics such as models of magnetic
storage devices as in computer memory.
Applications[edit]
Magnetostatics as a special case of Maxwell's equations[edit]
Starting from Maxwell's equations and assuming that charges are either fixed
or move as a steady current , the equations separate into two
equations for the electric field (see electrostatics) and two for the magnetic
field. The fields are independent of time and each other. The magnetostatic
[2]
equations, in both differential and integral forms, are shown in the table below.
Form
Name
Differential Integral
Gauss's law
for magnetism
Ampère's law
Where ∇ with the dot denotes divergence, and B is the magnetic flux density,
the first integral is over a surface with oriented surface element
. Where ∇ with the cross denotes curl, J is the current density and H is
the magnetic field intensity, the second integral is a line integral around a
closed loop with line element . The current going through the
loop is .
The quality of this approximation may be guessed by comparing the above
equations with the full version of Maxwell's equations and considering the
importance of the terms that have been removed. Of particular significance is
the comparison of the term against the term. If the
