To provide power to a moving vehicle without using contacts, a transformer is presented, consisting of a fixed primary winding, inductively coupled to a moving secondary winding. The primary winding along the whole trajectory of motion is configured such that its magnetic stray field and its self inductance are limited. This winding transfers power to the moving coupler containing the yoke and the secondary winding. The secondary winding is a resonant circuit, with a rectifier and the motor of the vehicle as load. To describe the energy transmission system, a numerical model is developed that combines an electrical circuit with a 2D nonlinear finite element model. This model is used for an optimization of the design. For the optimized configuration, an experimental setup is built to validate the model by measurements. A sensitivity analysis is carried out concerning the primary current, the supply frequency, the position of the secondary winding relative to the primary winding and the number of vehicles coupled with the primary winding.