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Battery electric vehicles (BEVs) have emerged as a promising alternative to traditional internal combustion engine (ICE) vehicles due to benefits in improved fuel economy, lower operating cost, and reduced emission. BEVs use electric motors rather than fossil fuels for propulsion and typically store electric energy in lithium-ion cells. With rising concerns over fossil fuel depletion and the impact of ICE vehicles on the climate, electric mobility is widely considered as the future of sustainable transportation. BEVs promise to drastically reduce greenhouse gas emissions as a result of the transportation sector. However, mass adoption of BEVs faces major barriers due to consumer worries over several important battery-related issues, such as limited range, long charging time, lack of charging stations, and high initial cost. Existing solutions to overcome these barriers, such as building more charging stations, increasing battery capacity, and stationary vehicle-to-vehicle (V2V) charging, often suffer from prohibitive investment costs, incompatibility to existing BEVs, or long travel delays. In this paper, we propose Peer-to-Peer Car Charging (P2C2), a scalable approach for charging BEVs that alleviates the need for elaborate charging infrastructure. The central idea is to enable BEVs to share charge among each other while in motion through coordination with a cloud-based control system. To re-vitalize a BEV fleet, which is continuously in motion, we introduce Mobile Charging Stations (MoCS), which are high-battery-capacity vehicles used to replenish the overall charge in a vehicle network. Unlike existing V2V charging solutions, the charge sharing in P2C2 takes place while the BEVs are in-motion, which aims at minimizing travel time loss. To reduce BEV-to-BEV contact time without increasing manufacturing costs, we propose to use multiple batteries of varying sizes and charge transfer rates. The faster but smaller batteries are used for charge transfer between vehicles, while the slower but larger ones are used for prolonged charge storage. We have designed the overall P2C2 framework and formalized the decision-making process of the cloud-based control system. We have evaluated the effectiveness of P2C2 using a well-characterized simulation platform and observed dramatic improvement in BEV mobility. Additionally, through statistical analysis, we show that a significant reduction in carbon emission is also possible if MoCS can be powered by renewable energy sources.