The behaviour of electric and magnetic fields, whether in cases of electrostatics, magnetostatics, or electrodynamics ( electromagnetic fields ), is governed by Maxwell's equations.
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The behaviour of electric and magnetic fields, whether in cases of electrostatics, magnetostatics, or electrodynamics ( electromagnetic fields ), is governed by Maxwell's equations:
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The Coulomb gauge is chosen in such a way that \ mathbf \ nabla \ cdot \ mathbf A'= 0, which corresponds to the case of magnetostatics.
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In magnetostatics, the force of attraction or repulsion between two current-carrying wires ( see first figure below ) is often called "'Amp�re's force law " '.
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(where ? is the Dirac delta function ), using the fact that the divergence of "'J "'is zero ( due to the assumption of magnetostatics ), and performing an integration by parts, the result turns out to be
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In magnetostatics where there is no time-varying charge distribution, only the first equation is needed . ( In the context of electrodynamics, the terms " vector potential " and " scalar potential " are used for " magnetic vector potential " and " electric potential ", respectively.
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Thus, electrostatics, as well as magnetism and magnetostatics, are now seen as studies of the static EM field when a particular frame has been selected to suppress the other type of field, and since an EM field with both electric and magnetic will appear in any other frame, these " simpler " effects are merely the observer's.
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:I'm taking your question to be a question purely about magnetostatics, since your question only mentions a magnetic field, not an electric field, and if you wanted to consider electromagnetic fields in general, then a laser beam would be the obvious example of an electromagnetic field that's in the form of a beam like a laser beam.
