A rubber flying ring having a diameter of (20 mathrm{~cm}) is fixed to the (x y)-plane of

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A rubber flying ring having a diameter of \(20 \mathrm{~cm}\) is fixed to the \(x y\)-plane of the Cartesian coordinate system such that its geometric center lies on the origin. The ring is uniformly charged with \(+10 \mu \mathrm{C}\).

(a) What is the magnitude of the electric field at \(10 \mathrm{~cm}\) on the z-axis?

(b) What is the magnitude of the electric field at the origin?

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