Obtain expressions for electric and magnetic fields in terms of scalar and vector potentials using homogeneous Maxwell's equations.
In classical electrodynamics, the electric and magnetic fields can be expressed in terms of the scalar potential \(\phi\) and vector potential \(\mathbf{A}\) by using the homogeneous Maxwell’s equations.
1. Magnetic Field (\(\mathbf{B}\)):
From Gauss's law for magnetism (\(\nabla \cdot \mathbf{B} = 0\)) and Ampère’s law in the absence of currents (\(\nabla \times \mathbf{B} = 0\)), we can express the magnetic field as the curl _______ __________ _______ __________ ______.
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and the retarded vector potential given by
,
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