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Work to Move parallel capacitor Plates

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Hi, in my book there are two capacitor plates distance x apart (they are kept connected to a constant voltage source). These plates are moved apart to distance 3x. In order to find the work done to move the capacitors apart (using W=F dl=QE dl), my book takes the charge Q of one plate and electric field felt on that one plate and integrates it from x to 3x. Why can't we take the take the charge and electric field felt on both plates and integrate half the distance of x to 3x?

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