The Answer: Solutions to Array of Capacitors Homework

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An infinite grid of identical 1-microFarad capacitors is connected to a battery across two distant junctions, creating a potential difference. The key finding is that the potential at any junction is the average of the potentials at its four nearest junctions. This relationship arises from the symmetry and uniformity of the capacitor arrangement, where each junction's net charge is influenced by its neighbors. The discussion emphasizes the importance of understanding the behavior of capacitors in an infinite array. The conclusion reinforces the concept of potential averaging in such configurations.
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Homework Statement



An infinite array of identical 1-microFarad capacitors are arranged in a grid setup, where junctions are between capacitors, and each junction is connected to 4 other junctions separated by another capacitor.

The array is initially uncharged. A battery is connected across two distant junctions.

Show that the potential at any junction is the average of the potential at the four nearest junctions.

(Hint: What is the net charge on any junction)

Homework Equations



V = Q/C
 
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Any chance that you could provide a figure. Perhaps you could scan one.
 
Sorry, I can't scan so I sloppily put together a picture:

http://imgur.com/k61zz

I'm assuming the junctions are the intersection points. All capacitors are the same.

EDIT: Also, it extends to infinity in every direction.
 

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