# Seems like Saturn

**Electricity and Magnetism**Level 4

At the origin of \(xyz\) coordinates there is a solid sphere with radius \(r\) and charge density \(\rho\). Around it, on \(xy\) plane, there is a ring with radius \(R\) and charge density \(\lambda\). If the magnitude of total electric field at \(P(0,0,H)\), such that \(H>r\), can be written as \[\dfrac{\rho \cdot r^3}{a\cdot H^2 \cdot \epsilon_{0}}+\dfrac{\lambda \cdot H\cdot R}{b\cdot (R^2+H^2)^{\frac{3}{2}} \cdot \epsilon_{0}}\] Find the value of \(a+b\)