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A magnetic field is a vector property of space that quantifies magnetic influence and governs forces/torques on charges, currents, and magnets, and can induce currents when time-varying.
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., \(\mathbf{N}=\mathbf{m}\times\mathbf{B}\)).
A magnetic field is a vector property of space that quantifies magnetic influence and governs forces/torques on charges, currents, and magnets, and can induce currents when time-varying.
Magnetic fields are produced by moving charges and magnetized materials, and are described using two related fields \(\mathbf{B}\) (flux density) and \(\mathbf{H}\) (field strength).
In vacuum \(\mathbf{B}=\mu_0\mathbf{H}\), while inside materials \(\mathbf{H}\) differs due to magnetization \(\mathbf{M}\); \(\mathbf{B}\) determines magnetic forces through the Lorentz force law and torques on dipoles through \(\mathbf{m}\times\mathbf{B}\).
A vector property of space that quantifies how magnetic influences act at each point, affecting moving charges, currents, and magnets.
The magnetic field vector \(\mathbf{B}\) that directly determines magnetic forces and torques, such as through the Lorentz force law.
The vector \(\mathbf{H}\) that represents magnetic field intensity and is related to \(\mathbf{B}\) and magnetization by \(\mathbf{H}\equiv\frac{1}{\mu_0}\mathbf{B}-\mathbf{M}\).
The vector \(\mathbf{M}\) describing how strongly a material becomes magnetized in response to an applied magnetic field.
The force on a moving charge in electromagnetic fields, including the magnetic contribution \(q(\mathbf{v}\times\mathbf{B})\).
The torque on a magnetic dipole moment \(\mathbf{m}\) in a magnetic field, given by \(\mathbf{N}=\mathbf{m}\times\mathbf{B}\).
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