Chapter 20, Problem 45GP

& A piece of wire, shown in Figure P20.45, moves downward perpendicular to a magnetic field. (a) In what direction will the electrons in the wire move? (b) After the electrons are forced in one direction, leaving positive charges behind. an $\stackrel{**\#x2192;}{E}$ field and potential difference $\Delta V$ develop from one end of the wire to the other. The electrons no longer move, since the electric and magnetic forces exerted on them balance. Show that this happens when the potential difference from one end of the wire to the other is $\Delta V=\nu LB$, where v is the speed of the wire, L is its length, and B is the magnitude of the magnetic field. Describe two real-world situations where this phenomenon might occur.

Figure P20.45