Concentric Spheres Capacitance Question- How to use area

In summary, the person is asking for help with solving a question involving three concentric metal shells being treated as two capacitors in series. They are wondering which area to use in the capacitance formula and if the equation assumes equal charge. They are advised to find the correct formula for a spherical capacitor in their textbook.
  • #1
swooshfactory
63
0

Homework Statement



I am trying to solve a question where I have three concentric metal shells at different radii. I am treating them as two capacitors in series. I would like to use the formula C= enot*area/distance between capacitors, but I have a few questions.



Homework Equations



(in next section)

The Attempt at a Solution



1. Which area would I use when computing the capacitance for between shells? I assume the smaller one, because I assume that if you put a small electrode over a larger electrode, the capacitor would only exist in the area between, making the smaller area the area to use.
2. Does this equation assume equal charge? No charge is used in the formula. However, the other formula I know for capacitance, C=Q/deltaV, would assume equal charge over both. Is this relevant for this problem?


Thanks for any help.
 
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  • #2
HI swooshfactory,

swooshfactory said:

Homework Statement



I am trying to solve a question where I have three concentric metal shells at different radii. I am treating them as two capacitors in series. I would like to use the formula C= enot*area/distance between capacitors

This is the capacitance formula for a parallel-plate capacitor; a spherical capacitor would have a different formula. Once you find that formula (it should be in your textbook) you'll be able to answer your questions.
 
  • #3




The formula you have provided, C= enot*area/distance between capacitors, is only applicable for parallel plate capacitors. For concentric spheres, the formula for capacitance is given by C= 4πenot*(a*b)/(b-a), where a and b are the radii of the inner and outer spheres, respectively. This formula assumes that the charge is evenly distributed on both spheres, so the answer to your second question is yes, it is relevant for this problem.

In terms of which area to use, you are correct in assuming that the smaller area should be used. This is because the electric field is stronger in the smaller area, and thus the capacitance will be larger. However, it is important to note that the formula for concentric spheres assumes that the area of the inner sphere is much smaller than the area of the outer sphere. If this is not the case, then the formula may not be accurate and a different approach may be needed.

I hope this helps you with your problem. Good luck with your homework!
 

1. How does the area affect the capacitance in a concentric spheres system?

The area of the spheres plays a crucial role in determining the capacitance in a concentric spheres system. The larger the area, the greater the capacitance, and vice versa. This is because a larger surface area allows for more charge to be stored, resulting in a higher capacitance value.

2. How do I calculate the capacitance in a concentric spheres system using the area?

To calculate the capacitance in a concentric spheres system using the area, you can use the following formula: C = 4πε0 (r1r2) / (r2 - r1), where r1 and r2 represent the radii of the inner and outer spheres respectively, and ε0 is the permittivity of free space.

3. How does the distance between the spheres affect the capacitance?

The distance between the spheres has an inverse relationship with the capacitance. As the distance increases, the capacitance decreases. This is because a larger distance between the spheres means that there is a smaller electric field between them, resulting in a smaller amount of charge being stored.

4. Can I use the area to determine the charge on the spheres in a concentric spheres system?

No, the area alone cannot determine the charge on the spheres. The charge on the spheres is determined by the voltage applied to the system and the capacitance. However, the area does play a role in determining the capacitance, which in turn affects the charge on the spheres.

5. How does the shape of the spheres affect the capacitance in a concentric spheres system?

The shape of the spheres does not affect the capacitance in a concentric spheres system. As long as the spheres are concentric, the capacitance will remain the same regardless of their shape. This is because the shape does not impact the area or the distance between the spheres, which are the two factors that determine the capacitance in this system.

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