Two rails of a railway track, insulated from both each other and the ground, are connected to a millivoltmeter. Determine the reading of the millivoltmeter when a train travels on the track at a speed of 180 km h ⁻¹ . The vertical component of the earth's magnetic field is 0.2 10⁻⁴ T and the rails are separated by 1 m .

Step-by-step solution

The speed of the train is v = 180 km h ⁻¹ = 180 5 18 m s ⁻¹ = 50 m s ⁻¹ . The axle of the train acts as a conductor of length l = 1 m moving with velocity v perpendicular to the vertical component of the earth's magnetic field B_v . The induced motional emf across the axle is given by: E = B_v l v Substituting the given values: E = (0.2 10⁻⁴ T ) (1 m ) (50 m s ⁻¹) E = 10 10⁻⁴ V E = 10⁻³ V = 1 mV The reading of the millivoltmeter is 1 mV .