Electric Field Symmetry in a Circular Charge Distribution

AI Thread Summary
The discussion revolves around a problem involving two uniformly charged curved rods forming a circle and the calculation of the electric field at the center of the circle. The key question raised is why the electric field at point P has only an x-axis component. It is clarified that the symmetry of the charge distribution leads to cancellation of the y-axis components of the electric field from opposite segments of the rods. A visual representation of the electric field vectors from small segments of the rods helps in understanding this cancellation. Ultimately, the symmetry of the circular charge distribution is crucial in determining the direction and magnitude of the electric field.
Martin V.
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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?
 

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I think the question means the angle the net E field makes with the positive x-axis (with the unit vector ##\hat{x}##).
 
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
 
Thanks #3 - with the drawing i found the reason :)
 
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