Find capacitance and charge of two aluminum electrodes

AI Thread Summary
To find the capacitance of two aluminum electrodes, each with a diameter of 3.0 cm and spaced 0.50 mm apart, the relevant formula is C=ε0A/d. The area A can be calculated using the surface area of a sphere, which is 4πR², where R is the radius of the spheres. The discussion highlights the challenge of applying the parallel plate capacitor formula directly due to the spherical shape, but it suggests that with two spherical shells of equal radii, the setup can be approximated as a parallel-plate capacitor. The problem's wording is noted as potentially misleading, emphasizing that capacitance pertains to both shells rather than just one.
David23454
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Homework Statement


Two 3.0-cm-diameter aluminum electrodes are spaced 0.50 mm apart. The electrodes are connected to a 200 V battery. Find the capacitance of one of the spheres.

Homework Equations


[/B]
C=QV
C=ε0A/d

The Attempt at a Solution


[/B]
I'm really not sure how to approach this problem. I tried solving the problem for the area of the sphere inserted into the formula, and when that turned out wrong, I then tried the volume, but the answers are not correct. I know that the formula C=ε0A/d is for a parallel plate capacitor, so I'm pretty sure I can't use it as is because I'm dealing with spheres, but I don't know where to start.
 
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does it have something to do with the electric field of a sphere E=Q/4πε0?
 
If there are two spherical shells of practically equal radii R then you can argue that this is essentially a parallel-plate capacitor with plate area = 4πR2 and separation 0.5 mm. In fact, the answer is very accurate since there are no fringing effects as in parallel-plate capacitors.

The problem is poorly worded so I'm guessing as to the two shells. Capacitance is for both shells, not just one ...
 
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