Constants in scalar and vector potentials

[struggling_student]

We have a scalar potential $$\Phi(\vec{r})=\frac{q}{4\pi\epsilon_0} \left( \frac{1}{r} - \frac{a^2\gamma e^{-\gamma t}\cos\theta}{r^3}\right)$$

and a vector potential $$\vec{A}(\vec{r})=\frac{a^2qe^{-\gamma t}}{4\pi\epsilon_0r^4}\left(3\cos\theta\hat{r} + \sin\theta\hat{\theta} \right) .$$

how do I interpret the constants $a$ and $\gamma$. Do they have any physical meaning or are they arbitrary, unmeasurable values?

 

[Delta2]

Focusing first on the formula for vector potential, we can say that $a$ is part of the amplitude while $\gamma$ is the attenuation factor (or the damping factor) with respect to time. In time $t=\frac{5}{\gamma}$ the amplitude loses 99.32% of its initial value at time t=0.

Similar things can be said for the $\frac{1}{r^3}$ term of the scalar potential.

As to if they are measurable things, yes they are. At least from what I know is that usually we can measure the scalar potential (not sure about the vector potential) and from that we can infer the values of a ang gamma.

P.S We can measure both scalar and vector potential but we have to use additional conditions (known as gauge conditions, e.g. Coulomb gauge, Lorentz gauge. In any case what we actually can measure is electric and magnetic field , $\vec{E},\vec{B}$.