Magnetostatic forces on a chain of spherical beads in a nonuniform magnetic field

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Abstract
An analysis is presented for calculating the magnetic forces at various joints of a chain of spherical beads in a magnetic field. A potential energy approach has been used. The analysis shows that the chain is markedly weak at the first joint even though it has the maximum magnetic field. Contrary to intuition, the second joint is the strongest. Therefore, the beads in a long chain can be removed one by one up to a point. An attempt to remove additional beads will break the chain at the first joint. The strength of the second joint can be varied and made weaker than the first joint when the beads are separated by a thick coating of paramagnetic material. The calculations are supported qualitatively by a simple experiment.