运动电动势

Motional EMF is a direct consequence of the Lorentz force acting on mobile charges inside a conductor that is moving relative to a magnetic field. As the conductor moves with velocity [latex]\mathbf{v}[/latex] through a magnetic field [latex]\mathbf{B}[/latex], the free charges (electrons) within it experience a magnetic force [latex]\mathbf{F}_m = q(\mathbf{v} \times \mathbf{B})[/latex]. This force is perpendicular to both the velocity and the magnetic field, causing the charges to accumulate at one end of the conductor, leaving the other end with a net positive charge. This charge separation creates an internal electrostatic field [latex]\mathbf{E}_e[/latex] that opposes the further migration of charges. Equilibrium is reached when the electrostatic force [latex]\mathbf{F}_e = q\mathbf{E}_e[/latex] exactly balances the magnetic force, i.e., [latex]q\mathbf{E}_e = -q(\mathbf{v} \times \mathbf{B})[/latex].

The effective electric field experienced by the charges, [latex]\mathbf{E}_{eff} = \mathbf{v} \times \mathbf{B}[/latex], is a non-conservative field that drives the current. The EMF is the work done per unit charge by this effective field integrated along the length of the conductor. For a straight wire of length [latex]L[/latex] moving perpendicular to a uniform field [latex]B[/latex], the EMF simplifies to [latex]\mathcal{E} = BLv[/latex]. While motional EMF can be seen as a specific case of Faraday’s law of induction (in terms of changing flux), the Lorentz force perspective provides a more microscopic explanation of the mechanism responsible for the charge separation and the resulting voltage.