Calculating Potential Difference in Suspended Capacitor

AI Thread Summary
To calculate the potential difference between the plates of a capacitor with a suspended charged object, one must consider the forces acting on the object, including gravitational force and the electric force due to the electric field. The angle \theta of the thread with the vertical is crucial for establishing the relationship between the mass m, charge q, plate separation d, and the electric field E. The equations ΔV = -Ed and CΔV = q are fundamental for relating voltage to electric field and charge. A free body diagram can aid in visualizing the forces, although the length of the thread is not provided. Understanding the balance of forces allows for the determination of the potential difference across the capacitor plates.
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Homework Statement



A small object of mass m carries charge q and is suspended by a thread between the vertical plates of a capacitor. The plate separation is d. If the thread makes an angle \theta with the vertical, what is the potential difference between the plates.

Homework Equations



\Delta V=-Ed
C\Delta V=q
E = kq/r^2
C = e0*A/d

The Attempt at a Solution


I drew a free body diagram, but since the length of the thread isn't given, it doesn't appear to help.
I'm having a hard time finding a relationship between theta, m, d, and q. Any hints?
 
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What is the relationship between the voltage on the plates and the electric field between them? What is the equation for the force on the charged mass due to the electric field? What is the force of gravity on the mass?
 
Got it now, thanks
 

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