Question

Two rails of a railway track insulated from each other and the ground are connected to a milli voltmeter. What is the reading of voltmeter, when a train travels with a speed of 180 km/hr along the track. Given that the vertical component of earth's magnetic field is 0.2×10⁻⁴ weber/m² and the rails are separated by 1 metre
(a) 10⁻² volt(b) 10⁻⁴ volt(c) 10⁻³ volt(d) 1 volt

Answer 1

answer : option (a) 10–² volts

it is given that, speed of train, v = 180 km/h = 180 × 5/18 = 50m/s

from data, vertical component of earth's magnetic field , $B$ = 2 × 10^-4 T

separation between two rails , l = 1m

The induced emf is generated is given by,

$\xi=-\frac{d\phi}{dt}$

= $-\frac{d(BA)}{dt}$

= -$B\frac{dA}{dt}$

length travelled by train in dt = v.dt

so, change in area in dt , dA = l(v.dt)

so, $\xi=-B\frac{l(v.dt)}{dt}$

hence, $\xi=-Blv$

= -2 × 10^-4 × 1 × 50

= -10^-2 volts

hence , magnitude of induced emf = 10^-2 volts

hence, option (a) is correct