The capacitance of the two metal sphere system

In summary: So, the capacitance will not be the same for two spheres with different charge densities on their surfaces.In summary, the capacitance of the two metal sphere system is two times the calculated potential with integration.
  • #1
Indis Nenhrma
8
0
the capacitance of two metal sphere system

Homework Statement



What is the capacitance of the two metal sphere system.

*The question has been attached shematically. All the variables are given in the attached file, there is no missing variable.

thx for any help.
 

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  • #2
I thought that I could solve this problem by integration. I can divide two spheres to small circular plates as parallel to each other and consider them as parallel plates. Then, i can add them up. It ain't difficult, but it requires calculus knowledge.
 
Last edited:
  • #3
You can't do it that way. It is a very difficult problem by any method.
You could try image, but a large number of image charges would be needed.
 
  • #4
Capacitance of two metal sphere system

You can find the electric-field due to one sphere. Then, intagrate it from r to L-r to find the potential between spheres due to one sphere. I think the spheres must have a charge +Q and -Q, thus, potentials due to each sphere are same and total potential is two times the calculated one with integration. Once you have found an equality consists of Q and V, you can find the capacitancy by writing this equality in form of Q = C*V.
 
  • #5
Porter said:
Then, intagrate it from r to L-r to find the potential between spheres due to one sphere.

Why did you choose limits as r and L-r?
 
  • #6
Because potential diffrence inside a sphere is zero, there is no potential difference between 0 and r, you do not need the to add potential difference between these points. And, of course, electric-field inisde sphere is zero, not depending on distance, so you can not even intagrate electric-field by choosing limits involving 0 to r and L-r to L intervals.
 
  • #7
thx dude.
 
  • #8
But the surface charge density on each sphere is not uniform.
 

What is the capacitance of the two metal sphere system?

The capacitance of a two metal sphere system refers to the ability of the system to store electric charge. It is a measure of the amount of charge that can be stored on the spheres for a given potential difference between them.

How is the capacitance of the two metal sphere system calculated?

The capacitance of the two metal sphere system can be calculated using the formula C = 4πε0(r1r2) / (r2 - r1), where r1 and r2 are the radii of the two spheres and ε0 is the permittivity of free space.

How does the distance between the two spheres affect the capacitance of the system?

The capacitance of the two metal sphere system is inversely proportional to the distance between the spheres. This means that as the distance between the spheres increases, the capacitance decreases.

What is the significance of the capacitance of the two metal sphere system?

The capacitance of the two metal sphere system is an important concept in understanding the behavior of capacitors and electrical circuits. It plays a crucial role in determining the amount of charge that can be stored and the potential difference between the spheres.

How does the material of the spheres affect the capacitance of the system?

The capacitance of the two metal sphere system is also affected by the material of the spheres. Different materials have different permittivity values, which can impact the capacitance of the system. Materials with higher permittivity will have a higher capacitance compared to those with lower permittivity.

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