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

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The discussion centers on the electric field direction of a ring with continuous polarization, specifically questioning whether it is downward at a point P located a distance d from the center. The instructor concluded that the field direction is downward, but there is skepticism regarding this interpretation. The concern is that as one moves around the ring, the z-direction components may not align with the assigned y-direction magnitude. This raises questions about the accuracy of the field direction assignment. Further clarification and ideas are sought to resolve the confusion.
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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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