Capacitance of three concentric spherical shells?

In summary, the conversation discusses finding the capacitance of three concentric spherical shells with outer radii a, b, and c. The relevant equations for this problem are E=-gradV and C=Q/V, with the latter being (4∏ε)/((1/a)-(1/b)) for two shells. The suggested solution involves finding the voltage between the two inner shells and then the two outer shells and adding them together.
  • #1
anban
20
0

Homework Statement



I do not have a specific question, I am just wondering how one would go about finding the capacitance of three concentric spherical shells. Suppose the outer radius of the each shell is a, b, and c from the center outwards.

Homework Equations



E= -gradV
C = Q/ V, which for two shells = (4∏ε)/ ((1/a)-(1/b)) ... this is the voltage between the two shells.

The Attempt at a Solution



If we found the voltage between the two inner shells and then the to outer shells, perhaps we could add them? What do you you all think?
 
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  • #2
You can add the voltages across series elements.

ehild
 

Related to Capacitance of three concentric spherical shells?

1. What is capacitance?

Capacitance is the ability of a system to store an electric charge. It is measured in farads (F).

2. How is capacitance of three concentric spherical shells calculated?

The capacitance of three concentric spherical shells can be calculated using the formula C = 4πε0(abc/a+b+c), where a, b, and c are the radii of the three shells and ε0 is the permittivity of free space.

3. What is the significance of three concentric spherical shells in capacitance?

Three concentric spherical shells are significant in capacitance because they create a unique and efficient way to store electric charge, allowing for a high capacitance value.

4. How does the distance between the shells affect the capacitance?

The distance between the shells has a direct impact on the capacitance. As the distance decreases, the capacitance increases because the electric field between the shells becomes stronger. As the distance increases, the capacitance decreases.

5. Can the capacitance of three concentric spherical shells be changed?

Yes, the capacitance of three concentric spherical shells can be changed by altering the radii of the shells or by changing the material between the shells. Additionally, the capacitance can be increased by adding more shells in the concentric arrangement.

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