Question

A train is running at a speed of \(72\ \text{km h}^{-1}\) on the rails separated by a distance of \(150\) cm. If the vertical component of earth's magnetic field at the place is \(4.0\times10^{-5}\) T. The induced emf on the rails is

• A. \(1.2\) mV
• B. \(3\) mV
• C. \(2.5\) mV
• D. \(0.5\) mV
• E. \(4.2\) mV

Hint:

In motional emf problems: \[ \mathcal{E}=Blv \] Convert speed from km/h to m/s first.

Answer 1

The Correct Option is A

Motional emf: \[ \mathcal{E}=Blv \] Given: \[ B=4.0\times10^{-5}\text{ T} \] \[ l=150\text{ cm}=1.5\text{ m} \] \[ v=72\text{ km h}^{-1}=20\text{ m s}^{-1} \] So, \[ \mathcal{E}=4.0\times10^{-5}\times 1.5\times 20 \] \[ \mathcal{E}=1.2\times10^{-3}\text{ V}=1.2\text{ mV} \] Hence, \[ \boxed{(A)\ 1.2\text{ mV}} \]