# Trivial Problem With An Arrange

A fixed solid sphere with radius $$R$$ and charge density given by $$\rho (r) = \dfrac{\rho_{0}}{r^2}$$ is placed at a distance $$2d$$ from a fixed particle with charge $$q$$ (from the center of the sphere). If at a distance $$x$$ from the fixed particle there is a point charge at equilibrium, then $$x$$ can be written as $\dfrac{ad\sqrt{q}}{b\sqrt{\pi R \rho_{0}}+\sqrt{q}}.$

Find the value of $$a+b$$.

Assume both of the fixed charges are of the same sign.

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