Chapter 30 - Induction and Inductance - Problems - Page 897: 18c

$n=1$

In part (a), we found that $A = h^2$, where $h$ is the height of the bar above the vertex. We can find the magnitude of the emf: $\mathscr{E} = \frac{d\Phi}{dt}$ $\mathscr{E} = \frac{dA}{dt}~B$ $\mathscr{E} = \frac{dA}{dh}~\frac{dh}{dt}~B$ $\mathscr{E} = (2h)~(v)~(B)$ $\mathscr{E} = (2vt)~(v)~(B)$ $\mathscr{E} = 2Bv^2~t$ If $~~\mathscr{E} = at^n,~~$ then $~~n=1$