Answer
We can rank the situations according to the magnitude of the net electric field:
$(3) \gt (1) = (2)$
Work Step by Step
We can consider the net electric field at point $P_1$
In case (1), the electric field from Ring A is directed to the right, while the electric field from Ring B is directed to the left. By symmetry, the magnitudes of these electric fields are equal so the net electric field is zero.
In case (2), the electric field from Ring A is directed to the left, while the electric field from Ring B is directed to the right. By symmetry, the magnitudes of these electric fields are equal so the net electric field is zero.
In case (3), the electric field from Ring A is directed to the left, while the electric field from Ring B is directed to the left. The magnitude of the net electric field is the sum of the magnitudes of the electric field due to Ring A and the electric field due to Ring B.
We can rank the situations according to the magnitude of the net electric field:
$(3) \gt (1) = (2)$
