How Is the Potential Difference Calculated in a Suspended Charge Scenario?

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To calculate the potential difference in a suspended charge scenario, the gravitational force acting on the charge and the electric force from the capacitor must be balanced. Given a point charge of mass 0.0836 kg and charge +6.84 μC at an angle of deflection θ = 22.3° between parallel plates separated by 0.0221 m, trigonometric relationships can be applied. The gravitational force can be calculated using F_gravity = m * g, while the electric force is derived from F_electric = q * E, where E is the electric field. By establishing the relationship between these forces and the geometry of the setup, the potential difference can be determined. This approach effectively combines physics principles to solve for the potential difference in the capacitor scenario.
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A point charge of mass 0.0836 kg and charge q = +6.84 μC is suspended by a thread between the vertical parallel plates of a parallel-plate capacitor, as shown in the figure below.


If the angle of deflection is θ = 22.3°, and the separation between the plates is d = 0.0221 m, what is the potential difference between the plates?


sorry it wouldn't let me paste the picture..
 
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If you know the gravitational force and most of the details about the electric force you can use trigonometry to figure out how they relate. How far are you?
 

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