Difficult# Ratio of the Charge on a Pair of Concentric Rings

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Figure 1 depicts a pair of charged, non-conducting rings which are concentrically arranged along a horizontal axis.

A field point lies halfway between the two rings, at a distance $h$ from the center of either ring. The radius of Ring 2, $\rho_2$, is three times the radius of Ring 1, $\rho_1$. A certain charge $q_1$ has been placed on Ring 1. You are charged with the task of determining how much charge to place on Ring 2, $q_2$, so that the electric field at the mid-point between the two rings is zero.

The correct ratio of charge on Ring 2 to the charge on Ring 1

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