Word Count : 563

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In classical electrodynamics, the scalar and vector potentials describe the electromagnetic field in terms of potentials from which the electric and magnetic fields can be derived. For an oscillating electric dipole, the electric and magnetic fields can be expressed in terms of these potentials, particularly at points far from the dipole, where the radiation fields are dominant.

### Oscillating Electric Dipole and the Potentials

Consider an oscillating electric dipole moment \(\mathbf{p}(t)\) located at the origin, defined as:

\[
\mathbf{p}(t) = p_0 \hat{z} \cos(\omega t),
\]

where \(p_0\) is the amplitude of the dipole moment, \(\hat{z}\) is the unit vector along the \(z\)-axis, and \(\omega\) is the angular frequency of oscillation.

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