Electric Field Symmetry in a Circular Charge Distribution

[Martin V.]

Homework Statement

Problem statement:
In the attached figure, two curved plastic rods, one of charge q and the other of
charge q, form a circle of radius R 8.50 cm in an xy plane. The x-axis passes
through both of the connecting points, and the charge is distributed uniformly on
both rods. If q 15.0 pC, what are the (a) magnitude and (b) direction (relative to
the positive direction of the x axis) of the electric field produced at P, the center of the circle?

Homework Equations

The Attempt at a Solution

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Read solution on Chegg.com
My question:
Why is it that the electric field only have a component in the x-axis?

 

[blue_leaf77]

I think the question means the angle the net E field makes with the positive x-axis (with the unit vector ##\hat{x}##).

 

[J Hann]

To get a better picture of the net field draw the electric field vector from a small segment of the curve
above the axis and the electric field vector from a corresponding segment below the x-axis

 

[Martin V.]

Thanks #3 - with the drawing i found the reason :)