The Hovering Magnetic Ring · AI Generator #GEN-392A6203

Physics · electromagnetism

Problem

A small permanent magnet shaped like a ring (mass

m = 2.4\;\text{g}

, inner radius

r = 0.5\;\text{cm}

) is placed around a vertical copper wire carrying a steady current

I = 12\;\text{A}

. The ring magnet has its magnetic dipole moment

\vec{\mu}

pointing vertically upward with magnitude

\mu = 0.18\;\text{A}\cdot\text{m}^2

. At what height

h

above the bottom end of the wire will the ring hover in equilibrium? Assume the wire extends from

z = 0

z = \infty

and the ring is centered on the wire. Take

g = 10\;\text{m/s}^2

and

\mu_0 = 4\pi \times 10^{-7}\;\text{T}\cdot\text{m/A}