Magnetic Field: B, H, Forces, and Sources

Magnetic field definition and physical role

In magnetism and electromagnetism, a magnetic field is a physical property of space that quantifies the magnetic influence at each location. It is represented mathematically as a vector field because both the strength and direction vary from point to point. Magnetic fields affect moving electric charges (including electric currents), exert torques on magnets, and can attract or repel magnets and magnetic materials; if the field changes with time, it can also induce electrical currents. Magnetic fields are created by moving charges and by magnetic (magnetized) materials. In the SI framework, two closely related vector fields are used: the magnetic flux density \(\mathbf{B}\) and the magnetic field strength \(\mathbf{H}\). In vacuum they are related by \(\mathbf{B}=\mu_0\mathbf{H}\), while inside materials they differ because \(\mathbf{H}\) accounts for the material’s magnetization \(\mathbf{M}\) (with \(\mathbf{H}\equiv\frac{1}{\mu_0}\mathbf{B}-\mathbf{M}\)). The physical role of \(\mathbf{B}\) is often defined through its ability to predict magnetic forces via the Lorentz force law, and it also determines torques on magnetic dipoles (e.g., \(\mathbf{N}=\mathbf{m}\times\mathbf{B}\)).

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B-field: magnetic flux density

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