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We said that the gravitational field inside a spherical shell is zero, and we proved it, obviously. The obvious reason was that the field gets cancelled at any point inside the hemisphere.

Going the same way, can we say that the field in the plane of a ring will be zero. If yes, than how can we prove it and if no, than what would be the field at any point having coordinates $(r, \theta)$?

Qmechanic
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KeSHAW
  • 45
  • what would be the field at any point having coordinates $(r,\theta)$? There isn’t a simple expression for it. You can write an integral for it, and the integral might be reducible to “special functions”, but these functions are really just names for integrals that don’t reduce to elementary functions. – Ghoster Oct 19 '22 at 16:16
  • See this for the potential in the plane of the ring. You can differentiate inside the integral to get the field. – Ghoster Oct 19 '22 at 16:24

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