The Electromagnetic Brake Pad · AI Generator #GEN-62292995

Physics · electromagnetism

Problem

A novel electromagnetic brake system uses a conducting disk that rotates between the poles of a strong permanent magnet. The disk has radius R=15  cmR = 15\;\text{cm} and thickness t=5  mmt = 5\;\text{mm}, and is made of aluminum with resistivity ρ=2.8×10−8  Ω⋅m\rho = 2.8 \times 10^{-8}\;\Omega \cdot \text{m}. The magnetic field is uniform with magnitude B=0.8  TB = 0.8\;\text{T} and is perpendicular to the disk surface, extending from radius r1=5  cmr_1 = 5\;\text{cm} to radius r2=12  cmr_2 = 12\;\text{cm}. When the disk rotates at angular velocity ω=50  rad/s\omega = 50\;\text{rad/s}, eddy currents are induced in the conducting material, creating a braking torque. Model the eddy currents as flowing in thin concentric rings within the magnetized region. Find the total braking torque acting on the disk.

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