Magnetic scalar potential
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Magnetic scalar potential,
Magnetic scalar potential[edit]
![](https://upload.wikimedia.org/wikipedia/commons/thumb/8/84/VFPt_flat_magnets_gap_potential%2Bcontour.svg/220px-VFPt_flat_magnets_gap_potential%2Bcontour.svg.png)
The scalar potential is a useful quantity in describing the magnetic field, especially for permanent magnets.
Where there is no free current,
so if this holds in simply connected domain we can define a magnetic scalar potential,
Using the definition of H: it follows that
Here, ∇ ⋅ M acts as the source for magnetic field, much like ∇ ⋅ P acts as the source for electric field. So analogously to bound electric charge, the quantity
is called the bound magnetic charge density. Magnetic charges never occur isolated as magnetic monopoles, but only within dipoles and in magnets with a total magnetic charge sum of zero. The energy of a localized magnetic charge qm in a magnetic scalar potential is
and of a magnetic charge density distribution
If there is free current, one may subtract the contributions of free current per Biot–Savart law from total magnetic field and solve the remainder with the scalar potential method.
See also[edit]
Notes[edit]
- ^ Vanderlinde 2005, pp. 194–199
References[edit]
- Duffin, W.J. (1980). Electricity and Magnetism, Fourth Edition. McGraw-Hill. ISBN 007084111X.
- Jackson, John David (1999), Classical Electrodynamics (3rd ed.), John Wiley & Sons, ISBN 0-471-30932-X
- Vanderlinde, Jack (2005). Classical Electromagnetic Theory. Bibcode:2005cet..book.....V. doi:10.1007/1-4020-2700-1. ISBN 1-4020-2699-4.