Question

The two rails of a railway track, insulated from each other and from the ground, are connected to a millivolt meter. What will be the reading of the millivolt meter when a train travels on the track at a speed of $180{\text{km h}}^{-1}$ ? The vertical component of earth's magnetic field is $0.2\times {10}^{-4}\text{T}$ and the rails are separated by $1\text{m}$.

• A. $2\text{mV}$
• B. $2.5\text{mV}$
• C. $1\text{mV}$
• D. $5\text{mV}$

Answer 1

The correct option is C $1\text{mV}$

Given:
$l=1\text{m};v=180{\text{km h}}^{-1}=50{\text{ms}}^{-1}$
$B_v=0.2\times {10}^{-4}\text{T}$

Where $B_v$ (vertical component of the earth's magnetic field) is the component of magnetic field in a direction perpendicular to the plane of the motion.

The train can be treated as a single conductor moving in a magnetic field.

Therefore, induced emf across its length is,

$E=Bvl$

$E=0.2\times {10}^{-4}\times 50\times 1$

$\therefore E=1\times {10}^{-3}=1\text{mV}$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(B\right)$ is the correct answer.

Why this question? This question connects the real life situations and the concept you learn in theories.