Picture an enormous square piece of aluminum sheet, say of $100x100(m^2)$, on which' two opposite corners we put a potential difference. The ensuing current is low enough to do no damage to the sheet or the voltage supplier.

How will the current distribution between the two points of the square, throughout the sheet, look like? Will the current be the highest on the diagonal, getting less approaching the edges of the sheet (and maybe be zero somewhere, which I can't imagine)?

I can remember from high school that according to Ohm's law $V=IR$ ($V$ being the potential difference, $I$ the current, and $R$ the resistance), and that by putting a piece of metal between the anode and cathode of a battery we can take $R=0$, so we short-circuit the battery, but because of the internal resistance of the battery, the current won't be infinite. In reality, this is, of course, not true, especially for such a big piece of metal as stated above. And in a structure as the big sheet of aluminum $I$ isn't a scalar but a vector $\vec I$ (it has a magnitude as well as a direction at every point of the sheet), which means $V$ becomes also a vector somehow.

Maybe we can compare the situation with a sheet of water between two closed, square pieces of glass with two little holes on two opposite sides of a diagonal, which we use (by connecting little water hoses to them) to create a pressure difference. By putting little, colored balls (with the same mass density as the water) in the water we can see the distribution of the water current between the two plates.

Is there a way to make the current in the aluminum visible? If so we can test the theoretical prediction of the current distribution, which is the core of my question.

Picture an enormous square piece of aluminum sheet, say of $100\times100(m^2)$, on which' two opposite corners we put a potential difference. The ensuing current is low enough to do no damage to the sheet or the voltage supplier.

How will the current distribution between the two points of the square, throughout the sheet, look like? Will the current be the highest on the diagonal, getting less approaching the edges of the sheet (and maybe be zero somewhere, which I can't imagine)?

I can remember from high school that according to Ohm's law $V=IR$ ($V$ being the potential difference, $I$ the current, and $R$ the resistance), and that by putting a piece of metal between the anode and cathode of a battery we can take $R=0$, so we short-circuit the battery, but because of the internal resistance of the battery, the current won't be infinite. In reality, this is, of course, not true, especially for such a big piece of metal as stated above. And in a structure as the big sheet of aluminum $I$ isn't a scalar but a vector $\vec I$ (it has a magnitude as well as a direction at every point of the sheet), which means $V$ becomes also a vector somehow.

Maybe we can compare the situation with a sheet of water between two closed, square pieces of glass with two little holes on two opposite sides of a diagonal, which we use (by connecting little water hoses to them) to create a pressure difference. By putting little, colored balls (with the same mass density as the water) in the water we can see the distribution of the water current between the two plates.

Is there a way to make the current in the aluminum visible? If so we can test the theoretical prediction of the current distribution, which is the core of my question.