Equivalent capacitance of a system of 2 spheres

In summary, the homework problem involves two widely separated conducting spheres of radii R1 and R2. Their individual capacitances can be calculated using the formula 4π εoR. When the spheres are connected by a wire, the combination is either connected in series or parallel. The text does not specify, but the answer suggests they are connected in parallel. In this case, the spheres will share the same potential and charges will flow until they reach the same potential.
  • #1
randomgamernerd
139
4

Homework Statement

: [/B]Two conducting spheres of radii R1 and R2 are kept widely separated from each other. what are their individual capacitances? If the spheres are connected by a metal wire, what will be the capacitance of the combiation?

Homework Equations


Capacitance of a sphere of radius R is 4π εoR

The Attempt at a Solution

: [/B]from the equation above,we get capacitance of each sphere. I have no issue with that. For the next part, I think the spheres are connected in series because they are connected by a single wire. But from the answer given in the text,it seems the spheres are connected in parallel. Can anyone please clarify in which combination they are connected?
No other information is mentioned in the text.
 
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  • #2
randomgamernerd said:
from the equation above,we get capacitance of each sphere. I have no issue with that. For the next part, I think the spheres are connected in series because they are connected by a single wire. But from the answer given in the text,it seems the spheres are connected in parallel. Can anyone please clarify in which combination they are connected?
When they are connected by the wire, will they be at different potentials (like series connected capacitors) or share the same potential (like parallel connected capacitors)?
 
  • #3
gneill said:
When they are connected by the wire, will they be at different potentials (like series connected capacitors) or share the same potential (like parallel connected capacitors)?
I think charges will flow till both reach the same potential
 
  • #4
ok..yeah right..they will have same potenial...so they are connected in parallel..ok i got it...thanks @gneill
 
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1. What is the formula for calculating the equivalent capacitance of a system of 2 spheres?

The formula for calculating the equivalent capacitance of a system of 2 spheres is C = 4πε₀r₁r₂ / (r₁ + r₂), where C is the equivalent capacitance, ε₀ is the permittivity of free space, and r₁ and r₂ are the radii of the two spheres.

2. How do you determine the capacitance of each individual sphere in the system?

The capacitance of each individual sphere can be determined using the formula C = 4πε₀r, where r is the radius of the sphere. This formula assumes that the spheres are isolated and not part of a larger system.

3. What factors affect the equivalent capacitance of a system of 2 spheres?

The equivalent capacitance of a system of 2 spheres is affected by the radii of the spheres, the distance between them, and the permittivity of the medium between them. It is also affected by any external factors, such as the presence of other nearby conductors.

4. Can the equivalent capacitance of a system of 2 spheres be greater than the capacitance of each individual sphere?

Yes, the equivalent capacitance of a system of 2 spheres can be greater than the capacitance of each individual sphere. This can happen if the spheres are close enough together and the permittivity of the medium between them is high enough.

5. Is the equivalent capacitance of a system of 2 spheres affected by the material of the spheres?

No, the material of the spheres does not affect the equivalent capacitance of the system. The only factors that affect the equivalent capacitance are the radii of the spheres, the distance between them, and the permittivity of the medium between them.

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