# Electric Field Locus

A solid infinite cylinder of equation $$x^2+y^2=R^2$$ has a uniform charge density $$\rho$$. It also has a spherical cavity which is represented by the equation $$x^2+y^2+z^2=R^2$$. The locus, in the $$xy$$ plane, where the electric field is maximum is a circle of radius $$\frac{a}{b}R$$, where $$a$$ and $$b$$ are coprime positive integers.

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

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