Find capacitance and charge of two aluminum electrodes

In summary, the problem involves two 3.0-cm-diameter aluminum electrodes spaced 0.50 mm apart and connected to a 200 V battery. The task is to find the capacitance of one of the spheres. The initial attempt at solving the problem using the formula C=ε0A/d for a parallel plate capacitor was incorrect, as this formula is not applicable for spheres. However, it is possible to treat the two spherical shells as a parallel plate capacitor with plate area of 4πR2 and separation of 0.5 mm, resulting in a very accurate answer due to the absence of fringing effects. This means that the capacitance is for both shells, not just one.
  • #1
David23454
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0

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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  • #2
does it have something to do with the electric field of a sphere E=Q/4πε0?
 
  • #3
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 ...
 

1. How do I find the capacitance of two aluminum electrodes?

To find the capacitance of two aluminum electrodes, you can use the formula C = Q/V, where C is the capacitance, Q is the charge, and V is the voltage. You will need to measure the voltage difference between the two electrodes and the amount of charge stored on them. Then, simply plug in the values into the formula to calculate the capacitance.

2. What is the unit of measurement for capacitance?

The unit of measurement for capacitance is farad (F). However, in most cases, you will be working with smaller values of capacitance, so you may need to use units like microfarad (μF) or picofarad (pF).

3. How do I measure the charge on the aluminum electrodes?

You can measure the charge on the aluminum electrodes by using a device called a charge meter or by using a multimeter in current mode. These tools can measure the amount of charge flowing through a circuit, and you can use them to measure the charge on the electrodes.

4. Can the capacitance of two aluminum electrodes change?

Yes, the capacitance of two aluminum electrodes can change depending on various factors. These factors include the distance between the electrodes, the material of the dielectric between the electrodes, and the voltage applied to the electrodes. As the distance between the electrodes increases, the capacitance decreases, and as the voltage increases, the capacitance increases.

5. What is the purpose of finding the capacitance and charge of two aluminum electrodes?

The purpose of finding the capacitance and charge of two aluminum electrodes is to understand the properties of a capacitor. Capacitors are essential components in many electronic circuits and are used to store and release electrical energy. By knowing the capacitance and charge of two aluminum electrodes, you can design and analyze circuits that use capacitors effectively.

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