The Levitating Magnet · AI Generator #GEN-495BAED1

Physics · electromagnetism

Problem

A small neodymium magnet (mass m=2.4  gm = 2.4\;\text{g}) is dropped from rest down the center of a vertical copper tube (inner radius R=1.2  cmR = 1.2\;\text{cm}, wall thickness t=1.0  mmt = 1.0\;\text{mm}). Due to electromagnetic induction, the magnet reaches a terminal velocity and appears to "float" down the tube slowly. The copper has resistivity ρ=1.7×10−8  Ω⋅m\rho = 1.7 \times 10^{-8}\;\Omega\cdot\text{m}. When the magnet moves at terminal velocity vtv_t, the induced electric field in the copper creates circular current loops that generate a magnetic flux opposing the magnet's motion. The magnitude of the induced electric field at radius rr from the tube axis is given by E(r)=B0vtr2RE(r) = \frac{B_0 v_t r}{2R}, where B0=0.15  TB_0 = 0.15\;\text{T} is the magnetic field strength of the magnet. Find the terminal velocity of the magnet.

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