I am trying to determine the size of a conductive 2-D sheet that has a specified degree of increased resistance (or reduced conductivity) compared to an infinite sheet.(adsbygoogle = window.adsbygoogle || []).push({});

Imagine that electrons enter the infinite sheet and exit the sheet at 2 points which are 1 unit of distance apart and aligned on the X axis. The sheet has a certain conductivity, for simplicity lets say it is 1.

There is a certain finite resistance that could be measured between the points (I don't think it would be zero!). What is the size and shape of an area that encloses 90% or 99% of the total current (again, for simplicity, lets say the voltage is 1)?

I have thought long and hard about the SHAPE of the "isocurrent" lines: Circular arcs? Canenarys? Parabolas? Elliptical arcs? And I have no idea what the answer is. Should the curve have a minimum length for a given enclosed area? Should any derivatives have a zero value or no discontinuities?

I had thought that if I could get a function for the shape of the isocurrent lines, then I could have a function for the length of the isocurrent line between the endpoints. Current is inversely proportional to the length of the isocurrent line, and I would hopefully be able to integrate the current as the center of the isocurrent line sweeps from a Y value of zero to infinity.

But I have come to a complete block. I thought that the isocurrent curves may be catenary lines, but the integral does not appear to converge on a finite value.

I am looking for guidance or a source for the answer.

-Tony

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Current flow in infinite sheet, and shape of isocurrents

Tags:

Loading...

Similar Threads for Current flow infinite |
---|

Will the maximum discharge current double for two parallel batteries? |

Induced Voltage from a current |

AC current flow |

Current flow in a two source circuit |

**Physics Forums | Science Articles, Homework Help, Discussion**