1. The problem statement, all variables and given/known data This isn't necessarily a question but something I found in my notes that I didn't understand. It says that from B = ∇ x A one can plug this into Faraday-Lenz's law ∇ x E = d(B)/dt and it leads to the equation: ∇ x (E + d(A)/dt)=0. From this is says "Using Helmholtz theorem, one can represent the curl free field as the gradient of a scalar potential." 2. Relevant equations B = ∇ x A ∇ x E = d(B)/dt ∇ x (E + d(A)/dt)=0 3. The attempt at a solution I know that in electrostatics the curl of the electric field is zero and hence there is a scalar potential associated such that E = -∇ V but I don't see the jump for the case involving the vector potential. Any guidance/explanation would be greatly appreciated.