The Electromagnetic Levitation Toy · AI Generator #GEN-7B850BB2

Physics · electromagnetism

Problem

A popular science demonstration involves levitating a small aluminum ring above an electromagnet. The electromagnet consists of a solenoid with N=800N = 800 turns, radius R=3.0  cmR = 3.0\;\text{cm}, and length L=15  cmL = 15\;\text{cm}. When AC current I(t)=I0sin⁡(ωt)I(t) = I_0 \sin(\omega t) with I0=5.0  AI_0 = 5.0\;\text{A} and ω=2π×60  Hz\omega = 2\pi \times 60\;\text{Hz} flows through the solenoid, it creates a time-varying magnetic field that induces currents in the aluminum ring. The aluminum ring has radius r=2.8  cmr = 2.8\;\text{cm}, cross-sectional area of the wire Awire=1.5×10−6  m2A_{wire} = 1.5 \times 10^{-6}\;\text{m}^2, and resistivity ρ=2.8×10−8  Ω⋅m\rho = 2.8 \times 10^{-8}\;\Omega\cdot\text{m}. The ring is positioned directly above the solenoid where the magnetic field can be approximated as uniform across the ring's area. Find the RMS (root-mean-square) value of the induced current in the aluminum ring. Use μ0=4π×10−7  H/m\mu_0 = 4\pi \times 10^{-7}\;\text{H/m}.

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