Dynamic wireless charging (DWC) is an emerging technology that enables the batteries of electric vehicles (EVs) to charge automatically while the vehicles are in motion. The DWC-EV system addresses the challenges inherent in battery technology, such as the short driving range, long recharging time, and high price. Compared with conventional plug-in EVs, the DWC-EV can charge a battery more frequently because it can be done while the EV is in motion from the charging infrastructure installed on the road. In this paper, we analyze how this frequent-charging characteristic of DWC-EV can affect the battery lifetime in the DWC-EV. We first introduce a mathematical model to evaluate the economic cost of the DWC-EV for a given battery size. A battery degradation model is incorporated to account for the quantitative relationship between the installation of the charging infrastructure and battery life extension. We then use the model to analyze how the economic cost varies with the size of the battery. Our preliminary findings provide insight into the relationship between DWC from the charging infrastructure and the battery's lifetime.