(Solved): The electric field between the plates of a parallel-plate capacitor is horizo ...

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The electric field between the plates of a parallel-plate capacitor is horizontal, uniform, and has a magnitude $$E$$. A small sphere of mass $$m=25.0\mathrm{g}$$ and charge $$q=?3.10\mathrm{uC}$$ is suspended by a thread between the plates, as shown in the figure below. Suppose the magnitude of the electric field $$E$$ is adjusted such that when the tension in the thread is $$0.253\mathrm{N}$$, the charge is in equilibrium. (a) Find the value of $$E$$. (b) Find the angle $$?$$ between the thread and the vertical. Hint: $${\sin }^2?+{\cos }^2?=1$$