Two thoughts:
1. Is your textbook using a c=1 convention? If not, then
2. You should be able to distinguish between those two potentials using dimensional analysis. The one you put forth has an extra sec/m multiplying it, but is otherwise the same.
I would post on the Physics help forum, but Latex does not work there! Perhaps a mathematician needs to help them out?
My text asks me to obtain the Lienard-Wiechert Potentials. The potentials are quoted as:
and
This seems wrong to me, I get the following
Is my text incorrect?
and can be combined into the 4-vector so I expect that and must have the same units (coulombs per meter). This is why I think the additional c is required and the text is wrong?
The text (Rindler; Relativity Special, General and Cosmological) does not use c=1.
I would agree that the components of a 4-vector must all have the same units. Otherwise, when you compute the dot product of a 4-vector with itself (thus producing a Lorentz invariant), you'd be adding up terms that didn't have the same units.
So the only question left is this: what are the units of ? If its units are, as I suspect, [m/s], then you are correct and the book must be wrong. If, on the other hand, is dimensionless, then the book is correct.
That's my verdict.