# Capacitance of parallel wires in checkerboard pattern

Below is a cross-sectional view of a 4x4 array of inter-meshed cylinders...

$$\begin{matrix}\Huge\circ && \Huge\bullet && \Huge\circ && \Huge\bullet \\\\ \Huge\bullet && \Huge\circ && \Huge\bullet && \Huge\circ \\\\ \Huge\circ && \Huge\bullet && \Huge\circ && \Huge\bullet \\\\ \Huge\bullet && \Huge\circ && \Huge\bullet && \Huge\circ \\\\ \end{matrix}$$

• $$\\Huge\circ\$$ & $$\\Huge\bullet\$$ are cylinders coming out of & into the screen, resp.
• Voltages $$\v_o\$$ & $$\v_i\$$ are applied to them, resp.
• Rows & columns are equidistant apart $$\d\$$ (measured centroid to centroid).
• All cylinders are same length $$\L\$$, dia. $$\D\$$, & overlap $$\O\$$.
• $$\O\lt L\$$.

How do I find the overall capacitance between them for a generalized nxn array?

• Sounds like a school assignment. What have you got thus far? – Oldfart Dec 8 '19 at 4:23
• It's not. I never had a question this difficult in undergrad lol I came up w/ it myself actually. – Landon Dec 8 '19 at 4:38
• Teach yourself to do field mapping by sketching the curvilinear squares. You can estimate capacitance of odd shapes quite well. Here is one example but search for more. – tomnexus Dec 8 '19 at 5:28