The Answer: Solutions to Array of Capacitors Homework

[GrantB]

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

 

[SammyS]

Any chance that you could provide a figure. Perhaps you could scan one.

 

[GrantB]

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.