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Assume a circuit placed in a magnetic field, that is connected to a voltage source(##\epsilon_1##) that would allow current flow, assume there is there is a Lorentz force(##F_L##) on the wire with length ##L## with respect to the magnetic field, and it starts to move. Based on the laws of electromagnetic induction, there is an induced ##-\epsilon##, with the original ##\epsilon_1## in that same conductor with length ##L##? How can they exist at the same time? I can't picture it... Induced EMF(from the voltage source) and back EMF from the electromagnetic induction due to the change in flux over time.

It somewhat helps to imagine it as two force vectors acting against one another and influencing the free charges, I know this incorrect, but it's my interpretation which I hope someone could enlighten me with.