Question

The wire $\text{PQ}$ has mass $0.5\text{kg}$ and resistance $2\Omega$ can slide on the smooth, very long horizontal parallel rails separated by a distance of $1\text{m}$. The resistance of the rails is negligible. A uniform magnetic field of magnitude $0.6\text{T}$ exists in the rectangular region, and a resistance $3\Omega$ connects the rails outside the field region. At $t=0$, the wire $\text{PQ}$ is pushed towards the right with a speed $v=5\text{m/s}$. Find the current in the loop at an instant when the speed of the wire $\text{PQ}$ is $5\text{m/s}$.

• A. $0.6\text{A}$
• B. $1.2\text{A}$
• C. $3\text{A}$
• D. $2.4\text{A}$

Answer 1

The correct option is A $0.6\text{A}$

Emf induced across the wire at $t=0$,

$E=Bvl=0.6\times 5\times 1$

The equivalent circuit can be drawn as,


$\therefore$ Current in the loop will be,

$i=\frac{E}{R+r}$

$=\frac{3}{3+2}=0.6\text{A}$

Hence, $\left(A\right)$ is the correct answer.