1. Spectral resolution of the retarded potentials
LL2 Section 64

2. Electromagnetic waves were spectrally resolved in section 49.
Static fields were spectrally resolved in section 51.
Now, fields of moving charges will be spectrally resolved.

3. The Fourier components of the potentials are
Now, make a Fourier expansion of the sources of the fields, charge and current.
Each Fourier component of
is the source for the corresponding component of the field.

4. The retarded potentials were given in (62.9)
There is a phase that depends on the distance from the source point to the field point
Fourier component of scalar potential
Divide out the factor that oscillates in time.
Same recipe for the vector potential

5. The differential equation satisfied by the scalar potential for an arbitrary field is (62.3).
This equation must b e satisfied for each Fourier component separately.
Time dependence is gone.

6. Sub Fourier coefficient for charge density
Into expression for Fourier coefficient of potential
Restore prime

8. Periodic motion gives discrete frequencies w0. Period T = 2p/w0.
Spectral resolution contains integer multiples of the fundamental: n w0.