Question

The current generator $i_g$, shown in figure, sends a constant current $i$ through the circuit. The wire $ab$ has a length $l$ and mass $m$ slide on the smooth, horizontal rails connected to $i_g$. The entire system lies in a vertical magnetic field $B$. The velocity of the wire as a function of time is

• A. $\frac{ilBt}{m}$
• B. $\frac{ilBt}{2m}$
• C. $\frac{2ilBt}{m}$
• D. $\frac{ilBt}{3m}$
• E. $\frac{ilBt}{5m}$
  

Answer 1

The correct option is A $\frac{ilBt}{m}$

Force of the wire carrying current: $F=BiL$
Newtons second Law: $ma=BiL$
$a=\frac{BiL}{m}$
Newton's Equation of motion:
$v=u+at$
$u=0$
$v=\frac{Bilt}{m}$