Motion planning for mobile manipulators is challenging because of their high degrees of freedom. The most effective approach for the motion planning of a mobile manipulator is to consider the different characteristics of a mobile robot and a manipulator while planning and controlling each system separately. In a previous study, different characteristics were considered using virtual impedance. This method involves forming a virtual impedance relationship between the two subsystems, enabling the mobile robot to track the movement of the manipulator. However, this study had certain limitations. Firstly, this method is not applicable to non-holonomic mobile robots. Secondly, obstacle avoidance methods for mobile robots are not considered. To address these limitations, we propose a novel concept for our motion planner that is called the virtual impedance energy field (VIEF), which refers to the work and change in total energy. We solved the first limitation of the previous study by transforming the virtual impedance force into the VIEF. Moreover, by integrating an obstacle field with the VIEF and using it as a local costmap, the second limitation was addressed. To validate the performance of our motion planner, we conducted simulations in environments comprising obstacles, with straight and curved trajectories of the end-effector. We then analyzed the pose change graph of the mobile robot and end-effector, pose error of the end-effector, and velocity of the mobile robot. We therefore confirmed that the manipulator successfully followed the desired trajectory, while the mobile robot maintained a distance from the end-effector and avoided obstacles.