The two rails of a railway track, insulated from each other, and the ground, are connected to a millivoltmeter. What is the reading of the voltmeter when a train travels at a speed of 180 km h–1 along the track? Given vertical component of earth's magnetic field is and the separation between the rails = 1 m.

Solution

Here,
Speed of the train, $ν = \frac{180 \times 1000}{3600} = 50 m s^{- 1}$
Vertical component of earth's magnetic field, B_v = 0.2 x 10^–4 T
Seperation between the rails, l = 1 m

The induced emf generated is given by

$ε = - \frac{dϕ}{dt} = - \frac{d}{dt} (B A) = - B \frac{dA}{dt}$

where, A is the area and B is the magnetic field.

If l is the distance between the rails and v is the speed of the train, then

Induced emf, $e = - B l v$
$|e| = 0.2 \times 10^{- 4} \times 1 \times 50 = 1 \times 10^{- 3} V = 1 m V$

Hence, the millivoltmeter will read 1 mV.

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