I have that ∇2∅ = 0 everywhere. ∅ is a scalar potential and must be finite everywhere. Why is it that ∅ must be a constant? I'm trying to understand magnetic field B in terms of the Debye potentials: B = Lψ+Lχ+∇∅. I get this from C.G.Gray, Am. J. Phys. 46 (1978) page 169. Here they found that Lχ=0 and ∇∅=0 and therefore gives no contribution to B. any help?