Question

The wire $\text{PQ}$ has mass $0.5\text{kg}$, resistance $2\Omega$ and 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 of $3\Omega$ 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 acceleration of the wire at this instant.

• A. $0.36{\text{m/s}}^2$
• B. $0.72{\text{m/s}}^2$
• C. $2{\text{m/s}}^2$
• D. $0{\text{m/s}}^2$

Answer 1

The correct option is B $0.72{\text{m/s}}^2$

Emf induced in the circuit is,

$E=Blv=0.6\times 5\times 1=3\text{V}$

$\therefore$ Current flowing in the circuit is,

$i=\frac{E}{R+r}=\frac{3}{5}=0.6\text{A}$

$\therefore$ Force acting on the wire due to magnetic field,

$F_m=ilB=0.6\times 1\times 0.6$

$\Rightarrow F_m=0.36\text{N}$

$\therefore$ Accleration of the wire is,

$a=\frac{F_m}{m}=\frac{0.36}{0.5}$

$\therefore a=0.72{\text{m/s}}^2$

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