Is the E Field Direction Downward for a Ring with Continuous Polarization?

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SUMMARY

The discussion centers on the electric field direction for a ring with continuous polarization, specifically addressing a configuration where the upper half is positively charged and the lower half is negatively charged. The instructor concluded that the electric field at point P, located a distance d from the center of the ring, points downward. However, there is skepticism regarding this conclusion due to the presence of a z-direction component when considering the incremental angle dTHETA, which may affect the overall field direction.

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O.J.
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a ring whose upper half is continuously + and lower half is continuously - at a point P a distance d from the centre. Now our instructer solved it for us pointing that the direction of the field is downwards. but I am not convinced, because although the sine is contant, each time to move dTHETA u have a component in the z direction, while the magnitude we found was assigned a y direction only...:(:(
 
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any ideas?
 

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