# 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 $$a+b$$

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