Recently, adopting mobile energy chargers to replenish the energy supply of sensor nodes in wireless sensor networks has gained increasing attention from the research community. Different from energy harvesting systems, the utilization of mobile energy chargers is able to provide more reliable energy supply than the dynamic energy harvested from the surrounding environment. While pioneering works on the mobile recharging problem mainly focus on the optimal offline path planning for the mobile chargers, in this work, we aim to lay the theoretical foundation for the on-demand mobile charging (DMC) problem, where individual sensor nodes request charging from the mobile charger when their energy runs low. Specifically, in this work, we analyze the on-demand mobile charging problem using a simple but efficient Nearest-Job-Next with Preemption (NJNP) discipline for the mobile charger, and provide analytical results on the system throughput and charging latency from the perspectives of the mobile charger and individual sensor nodes, respectively. To demonstrate how the actual system design can benefit from our analytical results, we present two examples on determining the essential system parameters such as the optimal remaining energy level for individual sensor nodes to send out their recharging requests and the minimal energy capacity required for the mobile charger. Through extensive simulation with real-world system settings, we verify that our analytical results match the simulation results well and the system designs based on our analysis are effective.