Question

Consider the situation shown in the figure. The wire PQ has mass m, resistance r and can slide on the smooth horizontal parallel rails of separated by a distance $l$. The resistance of the rails is negligible . A uniform magnetic field B exist in the rectangular region and a resistance R connects the rails outside the field region. At t=0, the wire PQ is pushed towards right with a speed of $v_0$. Find
(a) the current in the loop in an instant when the speed of the wire PQ is v.
(b) the acceleration of the wire at this instant
(c) Velocity v as a function

Answer 1

(a) When the speed is $V$
$Emf=Blv$
Resistance $=r+R$
Current $=\frac{Blv}{r+R}$

(b) Force acting on the wire $F=ilB$
$F=\frac{BlvlB}{R+r}=\frac{{l^{2}B}^{2}v}{r+R}$
Acceleration on the wire $=\frac{F}{m}=\frac{{l^{2}B}^{2}v}{m(r+R)}$

(c) $v=v_0+at=v_0-\frac{{l^{2}B}^{2}vt}{m(r+R)}=v_0-\frac{{l^{1}B}^{2}x}{m(r+R)}$