An object with mass \(m\) and charge \(q\) is dropped on an infinite inclined plane which forms an angle \(\theta\) with the horizontal, in the presence of a constant magnetic field \(B_{0}\) which goes out the page. If the coefficient of friction between the plane and the object is \(\mu\), the maximum magnetic force can be written as \(\dfrac{mg}{\mu}(a-\mu b)\), find the value of \(a^2+b^2\)

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