Soution : field in a ring with a center opening

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Field at the center of a loaded ring having an opening.

And the xOy plane xOz are planes of symmetry of the distribution of loads, the electrostatic field must belong simultaneously to these two planes, so they intersect. The field at the point O is then carried by the right Ox.

Either elemental electrostatic field created by the length dl element centered at a point P on the charged circumference of the ring:

Given the symmetry of the charge distribution, only the component along Ox contributes to total field O. Where:

The resulting field component for O:

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