A Helmholtz coil is an arrangement of two circular coils that produces a magnetic field in the center which is locally uniform in direction and magnitude, or at least nearly so. The configuration is optimal when the radius of each coil is equal to the separation between coils.
If the coils were replaced with massive rings, would this also produce a locally uniform gravitational field in both direction and magnitude? Or would a different diameter to separation be better?
Is there a well-recognized name for this configuration of masses?
Answer
The charge moving in a circle produces a magnetic dipole, and it is the proximity of the two magnetic dipoles that produces an approximately constant magnetic field in between the two coils.
However a ring of matter does not produce a gravitational dipole, unsurprisingly since there is no such thing as a negative mass so the analogous gravitational dipole doesn't exist. Indeed at the point exactly between the two rings of matter the gravitational field would be zero since the gravitational attractions to the two rings would be equal and opposite.
The electromagnetic analogy would be to consider the electric field created by two charged rings. The geometry of this field would be the same the same as the geometry of the gravitational field created by two massive rings.
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