Charge Distribution on Two Neighboring Conductors

In summary, the question is asking about the charge distributions on two spherical conductors with radius r and charge +Q, with centers a distance d apart. The answer is that for d much greater than r, there will be a uniform charge distribution on each sphere. However, if d is just a bit bigger than 2r, the charge distribution will change due to repulsion between like charges at the closest point. This problem can be solved using a sequence of image charges, but it becomes increasingly complex as the distance decreases.
  • #1
conquerer7
26
0
Say you have two spherical conductors, of radius r, centers a distance d apart. Both have charges of +Q. What are the charge distributions on them?

My physics book more or less handwaves and says it'll be more or less unaffected, but is there a way to solve this exactly?
 
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  • #2
I haven't solved an problems like that in many,many years...but I can provide a bit of an insight:

are these solid or hollow conductors...?

anyway, Say d is much, much greater than r...there should be a uniform distribution on each sphere...now bring them close together, say d is just a bit bigger than 2 r so they are close...like charges will repel somewhat at the closest point, less so further...so it sure
seems like the charge distribution WILL change...I disagree it would be "unaffected".
 
  • #3
This problem can be solved with a sequence of image charges. It gets quite complicated, but for d>>a, the series converges fast.
 

Related to Charge Distribution on Two Neighboring Conductors

1. What is meant by "charge distribution" on two neighboring conductors?

Charge distribution refers to the way in which electric charge is distributed across the surface of a conductor. In the case of two neighboring conductors, this refers to the amount and arrangement of positive and negative charges on each conductor.

2. How does charge distribution affect the behavior of two neighboring conductors?

The charge distribution on two neighboring conductors determines the strength and direction of the electric field between them. This can impact the flow of electric current and the overall behavior of the conductors.

3. What factors influence the charge distribution on two neighboring conductors?

The charge distribution on two neighboring conductors is influenced by the amount of charge present on each conductor, the distance between them, and the material properties of the conductors, such as their conductivity and shape.

4. How does the charge distribution change when the distance between the two conductors is altered?

The charge distribution on two neighboring conductors changes when the distance between them is altered. As the distance decreases, the electric field between the conductors becomes stronger, leading to a redistribution of charge. Similarly, increasing the distance between the conductors weakens the electric field and can result in a different charge distribution.

5. How is the charge distribution on two neighboring conductors related to the concept of capacitance?

Capacitance is a measure of the ability of two conductors to hold opposite charges and store electric potential energy. The charge distribution on two neighboring conductors directly affects the capacitance between them, as the amount and arrangement of charges impacts the strength of the electric field and the ability to store electric potential energy.

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