Chapter 30, Problem 58EAP

]58. You’ve decided to make the magnetic projectile launcher shown in FIGURE P30.58 for your science project. An aluminum bar of length l slides along metal rails through a magnetic field B. The switch closes at $t=0\text{ s}$ , while the bar is at rest, and a battery of emf ${\epsilon }_{\text{bat}}$starts a current flowing around the loop. The battery has internal resistance r. The resistances of the rails and the bar are effectively zero.

a. Show that the bar reaches a terminal speed $v_{\text{term}}$ and find an expression for $v_{\text{term}}$ .

b. Evaluate $v_{\text{term}}$ for ${\epsilon }_0=1.0\text{V}$ , $r=0.10\Omega$ , $l=6.0\text{cm}$ and $B=0.50\text{T}$ .