The Magnetic Levitation Train Detector · AI Generator #GEN-F4DAB773

Physics · electromagnetism

Problem

A magnetic levitation train uses superconducting magnets that create a strong, uniform magnetic field of magnitude

B = 0.80\;\text{T}

extending horizontally for a distance

L = 50\;\text{m}

along the track. To detect the train's position, engineers install a circular conducting loop of radius

r = 1.2\;\text{m}

and resistance

R = 0.15\;\Omega

positioned vertically beside the track. The loop's center is initially

d_0 = 3.0\;\text{m}

from the edge of the magnetic field region. When the train passes, it carries this magnetic field with it at a constant speed

v = 120\;\text{m/s}

. The magnetic field has sharp boundaries and can be considered to switch from zero to

B

instantaneously as the train approaches, and from

B

to zero as it recedes. Find the total electrical energy dissipated in the loop during the entire passage of the train.