1. The problem statement, all variables and given/known data Prove that a current density J(r, t) such that ∇ × J = 0 implies the magnetic field B = 0. 2. Relevant equations Maxwell's equations, vector calculus 3. The attempt at a solution I've played around with Maxwell's equations and with the properties of vector calculus but I can't reach the necessary conclusion. Any hints would be greatly appreciated.