In this paper, we use the retarded potential to solve the traveling field problem proposed by Feynman in his lectures on physics. Compared with general electromagnetic radiation problems, the retarded potential solution has the following characteristics in this particular problem: (1) the retarded potential is simple to integrate, and an exact analytical solution can be obtained; (2) the physical idea is clear, and the physical concept of "electromagnetic action propagates with finite speed" contained in the retarded potential formula is fully demonstrated in the solving process.