Scalar and Vector Potentials of a Charge at Rest

In order to derive expressions for the scalar and vector potentials produced by particle 2 we choose a frame of reference IS which is most suitable for this purpose. This is the case when IS is moving with the same speed, v, in the same direction as particle 2, 

Since particle 2 is observed to be at rest in IS, the vector potential in this frame of reference vanishes 

The first charge experiences a stationary potential ip2 r, t ) = (p2 r ) of the resting charge q2 so that the electromagnetic interaction energy between charge qi at position and charge qi at position in IS reads 

A note on retardation in IS is advisable. The transmission of the electrostatic interaction takes time, i.e., it is retarded. But since, according to Eq. 

the particular choice of IS has the advantage that the interaction energy is not affected by retardation effects. The reason for this is simply that the field experienced by charge 1 at time when this charge is at position has been transmitted by charge 2 at time The retardation time fj2 be calculated from the expression 

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