Motion planning is challenging for multiple robots in cluttered environments without communication, especially in view of real-time efficiency, motion safety, distributed computation, and trajectory optimality, etc. In this paper, a reinforced potential field method is developed for distributed multi-robot motion planning, which is a synthesized design of reinforcement learning and artificial potential fields. An observation embedding with a self-attention mechanism is presented to model the robot-robot and robot-environment interactions. A soft wall-following rule is developed to improve the trajectory smoothness. Our method belongs to reactive planning, but environment properties are implicitly encoded. The total amount of robots in our method can be scaled up to any number. The performance improvement over a vanilla APF and RL method has been demonstrated via numerical simulations. Experiments are also performed using quadrotors to further illustrate the competence of our method.