How the current steadily flows due to motional EMF?

Question

In motional EMF, the positive charges (current) flows from higher to lower potential. If this is the case, then the current should stop at the point of lower potential. But this does not happen - the current continues to flow. Why?

Answer 1

Perhaps considering a simple symmetrical set-up will help. A bar magnet is placed lengthwise on the axis of a circular wire loop, some way from the loop. We now move the loop steadily closer to the magnet at speed $v$.

The free electrons in the wire experience magnetic Lorentz forces, given by $$\mathbf F=(-e)\mathbf v \times \mathbf B$$ It is these forces that drive the free electrons round the loop. The field lines from the magnet 'splay out' and if, in the vicinity of the loop, they make an angle $\theta$ with the loop axis, the magnitude of the tangential force on the electrons in the loop will be $evB\sin\theta$. The emf is given by $$|\mathscr E|=\frac {\text{work done on electron per circuit of the loop}}e=\frac{evB\sin\theta \times 2\pi r}e=2\pi rvB\sin\theta$$ Notes

(a) This is the motional emf that you asked about. The force giving rise to the emf is a magnetic force. If we'd kept the wire stationary and moved the magnet, the force would be an electric one, due to a non-conservative electric field set up according to $$\mathbf{\nabla}\times\mathbf E=-\frac{d\mathbf B}{dt}.$$ Re-assuringly, we get the same size of the emf when it is calculated in this way (that is in the frame of reference in which the wire is stationary), as the Principle of Relativity demands.

(b) $2\pi rv$ is the rate of sweeping out of area (a cylindrical band) by the loop. $B\sin\theta$ is the component of magnetic flux density normal to this area, so $2\pi rvB\sin\theta$ is the rate of cutting of flux by the loop, which is (using $\mathbf{\nabla}.\mathbf B =0$) the rate of change of flux through the loop. So we can cast our equation for $|\mathscr E|$ into the familiar Faraday form, $$|\mathscr E|= \frac{d\Phi}{dt}.$$

(c) Note that, even if we move the loop towards the magnet at constant speed, $v$, the emf will not be constant. This is because $B\sin\theta$ increases as the loop approaches the magnet.

Answer 2

Because the current also flows through the battery. Actually in metallic conductors, it is the electrons which flows through the conductor. Read the mechanism of any simple cell, e.g. Electrochemical cell. If the elctrons were not to flow through the battery then they would eventually diminish the charge at cathode and anode of the battery. Then the internal chemicals will agitate again to make cathode negative and anode positive untill the reaction is exothermic.