# Motional EMF and Conservation of energy

Consider a conducting rod moving in a uniform magnetic field $\vec{B}$ with a uniform velocity $\vec{v}$. According to the theory involved, the electrons experience the magnetic force ($-e\cdot\vec{v}\times\vec{B}$) and will shift to one end of the rod, creating a positive charge on one side and negative on another.

This causes the existence of Electric Field and hence the potential energy associated with it. $\vec{B}$ does no work on the electrons or any of the charged particles. Therefore no work has been done in moving the charges to the places they have moved. But the charge separation has a potential energy which is greater than when the conductor was neutral. Therefore, it seems now that without doing any work, we have "created" energy in the form of potential energy. Where is the fallacy in this thinking?

• "... B⃗ does no work on the electrons or any of the charged particles. Therefore no work has been done" that is invalid reasoning. Magnetic has not done work, that's true, but the agent that made the rod move did work on the rod and the rod did work on the charges. – Ján Lalinský Jul 20 '15 at 19:10