Answer
$-90^{\circ}$
Work Step by Step
We make the assumption that bead 2 is in the lower half of the circle, partly because it would be awkward for bead 1 to “slide through” bead 2 if it were in the path of bead 1 (which is the upper half of the circle) and partly to eliminate a second solution to the problem (which would have opposite angle and charge for bead 2). We note that the net y component of the electric field evaluated at the origin is negative (points down) for all positions of bead 1, which implies (with our assumption in the previous sentence) that bead 2 is a negative charge.
When bead 1 is on the +y axis, there is no x component of the net electric field, which implies bead 2 is on the –y axis, so its angle is –90°
