Question

Magadh express takes $16$ hours to cover the distance of $960\text{km}$ between Patna and Ghaziabad. The rails are separated by $130\text{cm}$ and the vertical component of the earth's magnetic field is $4.0\times {10}^{-5}\text{T}$. Find the average emf induced across the width of the train.

Assume uniform non-stop motion.

• A. $4.3\times {10}^{-4}\text{V}$
• B. $2.1\times {10}^{-4}\text{V}$
• C. $5.5\times {10}^{-4}\text{V}$
• D. $8.7\times {10}^{-4}\text{V}$

Answer 1

The correct option is D $8.7\times {10}^{-4}\text{V}$

As the train moves in a magnetic field, a motional emf $(\epsilon =Bvl)$ is produced across its width.

Here, $B$ is the component of the earth's magnetic field in a direction perpendicular to the plane of the motion.

The speed of the train is,

$v=\frac{960\times {10}^3}{16\times 60\times 60}=16.67{\text{ms}}^{-1}$

Thus,

$\epsilon =4.0\times {10}^{-5}\times 16.67\times 1.30=8.7\times {10}^{-4}\text{V}$