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Continuous charge distribution. The volume charge density ρ is the amount of charge per unit volume (cube), surface charge density σ is amount per unit surface area (circle) with outward unit normal nĚ‚, d is the dipole moment between two point charges, the volume density of these is the polarization density P.
Gauss's law for magnetism: magnetic field lines never begin nor end but form loops or extend to infinity as shown here with the magnetic field due to a ring of current. Gauss's law for magnetism states that electric charges have no magnetic analogues, called magnetic monopoles; no north or south magnetic poles exist in isolation. [3]
These equations can be simplified by taking advantage of the fact that the electric and magnetic fields are physically meaningful quantities that can be measured; the potentials are not. There is a freedom to constrain the form of the potentials provided that this does not affect the resultant electric and magnetic fields, called gauge freedom.
But, when a magnet is placed in the non-uniform field, such as that due to another magnet, the pole experiencing the large magnetic field will experience the large force and there will be a net force on the magnet. If the magnet is aligned with the magnetic field, corresponding to two magnets oriented in the same direction near the poles, then ...
The magnetic field of larger magnets can be obtained by modeling them as a collection of a large number of small magnets called dipoles each having their own m. The magnetic field produced by the magnet then is the net magnetic field of these dipoles; any net force on the magnet is a result of adding up the forces on the individual dipoles.
The magnetization field or M-field can be defined according to the following equation: = Where d m {\displaystyle \mathrm {d} \mathbf {m} } is the elementary magnetic moment and d V {\displaystyle \mathrm {d} V} is the volume element ; in other words, the M -field is the distribution of magnetic moments in the region or manifold concerned.
The magnetic field between poles (see the figure for Magnetic pole model) is in the opposite direction to the magnetic moment (which points from the negative charge to the positive charge), while inside a current loop it is in the same direction (see the figure to the right). The limits of these fields must also be different as the sources ...
The original form of Maxwell's circuital law, which he derived as early as 1855 in his paper "On Faraday's Lines of Force" [9] based on an analogy to hydrodynamics, relates magnetic fields to electric currents that produce them. It determines the magnetic field associated with a given current, or the current associated with a given magnetic field.