The Levitating Paperclip · AI Generator #GEN-68BF01E1

Physics · electromagnetism

Problem

A science museum demonstration uses an electromagnet to levitate a small steel paperclip. The paperclip has a mass of

m = 0.80\;\text{g}

and is held suspended

d = 2.0\;\text{cm}

below the electromagnet's pole face. When the electromagnet is turned on, it creates a magnetic dipole moment in the paperclip of magnitude

\mu = 1.2 \times 10^{-4}\;\text{A}\cdot\text{m}^2

. The magnetic field varies with distance

z

below the pole face according to

B(z) = B_0 e^{-z/\lambda}

, where

B_0 = 0.15\;\text{T}

and

\lambda = 1.5\;\text{cm}

. For stable levitation, the magnetic force must exactly balance the gravitational force. What is the required magnetic field strength

B

at the paperclip's position?