Hello there,
This question comes up from time to time, and i was just taking another look at it recently.
The main question is that we have a square conducting sheet of uniform thickness and we apply one or more voltages to the sheet and then measure a point (or two) inside the square. We hope to be able to figure out where the point is located on the square.
Starting with two strips of conductive material, longer than wide, we have a resistance along the length of each one. The resistances are equal, and we measure by placing 1v at one end of each strip and 0v at the other end of each strip.
Any voltage measured along the strip shows that the gradient is linear, so if we measure half way across the strip we see 1/2 the voltage.
But now place the two strips side by side so that their edges touch electrically and perfectly. Do we still get the same results? Maybe so for this over simplified example, but take many strips and place them side by side and the Laplace equation says that we dont get the same results because there is action along the horizontal as well as along any line where the two potentials are placed. In other words, the field spreads out.
What do you think?
This question comes up from time to time, and i was just taking another look at it recently.
The main question is that we have a square conducting sheet of uniform thickness and we apply one or more voltages to the sheet and then measure a point (or two) inside the square. We hope to be able to figure out where the point is located on the square.
Starting with two strips of conductive material, longer than wide, we have a resistance along the length of each one. The resistances are equal, and we measure by placing 1v at one end of each strip and 0v at the other end of each strip.
Any voltage measured along the strip shows that the gradient is linear, so if we measure half way across the strip we see 1/2 the voltage.
But now place the two strips side by side so that their edges touch electrically and perfectly. Do we still get the same results? Maybe so for this over simplified example, but take many strips and place them side by side and the Laplace equation says that we dont get the same results because there is action along the horizontal as well as along any line where the two potentials are placed. In other words, the field spreads out.
What do you think?