# A Hard Kind Of Ring

A sphere of radius $$2\text { m}$$ translates around a fixed point at a distance of $$10\text{ m}$$ from the center of the sphere on the $$xy$$ plane, generating a solid toroid. If the toroid has constant density of charge $$125 \dfrac{C}{\text{m}^3}$$, the value of the electric field on the point $$P(0,0,5)$$ (where units are in meters) can be written as $$\dfrac{a\pi}{b\epsilon_{0}}$$ where $$a$$ and $$b$$ are coprime positive integers, find the value of $$a+b$$.

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