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Question
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 18 km h−1 along the track? Given vertical component of earth's magnetic field = 0.2×10−4 T and the separation between the rails = 1 m.
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 18 km h−1 along the track? Given vertical component of earth's magnetic field = 0.2×10−4 T and the separation between the rails = 1 m.
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Solution
The correct option is A 1 mV
The induced emf generated is given by
e=−dϕdt=−ddt(BA)=−BdAdt
where A is the area and B, the magnetic field. If l is the distance between the rails and v, the speed of the train, then
d Ad t=l v, ∴ e=−B l vHere l=1 m and B=0.2×10−4T.But we have v=180×10003600=50 m s−1|e|=0.2×10−4×1×50=1×10−3 V=1 mV
Hence, the millivoltmeter will read 1 mV
The induced emf generated is given by
e=−dϕdt=−ddt(BA)=−BdAdt
where A is the area and B, the magnetic field. If l is the distance between the rails and v, the speed of the train, then
d Ad t=l v, ∴ e=−B l vHere l=1 m and B=0.2×10−4T.But we have v=180×10003600=50 m s−1|e|=0.2×10−4×1×50=1×10−3 V=1 mV
Hence, the millivoltmeter will read 1 mV
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