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The fundamental equations magnetostatics are linear equations,
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The principle of superposition holds.
The magnetostaticstatic force on a particle with charge q is
(SI units),
(Gaussian units).
| Drift velocity: |  N = number of charge carriers |
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| Current density: |  |
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| Current: |  |
The continuity equation is
In statics 
.
 (SI units) |
 (Gaussian units) |
In situations with enough symmetry Ampere’s law alone can be used to find the
magnitude of B. The flux of B through any closed surface is zero.
| (SI units) | (Gaussian units) | |
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| For filamentary currents we have | ||
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.
A is not unique. 
, with
an arbitrary scalar field and C an arbitrary
constant vector is also a vector potential for the same field.
In magnetostatics we choose 
Then
| (SI units) | Gaussian units) | |
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The uniqueness theorem
:If A or its normal derivatives are specified at the boundaries of a volume V, then a unique solution exists for A inside V.
| (SI units) | (Gaussian units) | |
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| A is continuous across the boundary. | A is continuous across the boundary. |
| (SI units) | (Gaussian units) | |
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| For filamentary currents we have | ||
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| (SI units) | (Gaussian units) | |
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| The vector potential of a magnetic dipole at the origin is | ||
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| The magnetic field of a magnetic dipole at the origin is | ||
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The energy of a magnetic dipole in an external magnetic
field is 
This is the mechanical
work done to bring the dipole from infinity to its present position.
The force on a dipole is
.
The torque on a dipole is
.
The magnetization 
is defined as the magnetic dipole moment per
unit volume.
The total current density is due to free and to magnetization current densities.
| (SI units) | Gaussian units) | |
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 This definition is not unique. |
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For linear, isotropic, homogeneous (lih) magnetic materials we have:
| (SI units) | (Gaussian units) | |
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for diamagnetic
materials, 
for paramagnetic
materials, permanent magnets are not lih.
Boundary conditions for H
:
(SI units),
(Gaussian units),
in general.
