# A Hard Kind Of Ring

**Electricity and Magnetism**Level 5

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 \(a+b\).