A Physics Puzzle from the Kitchen (sort of)

Diagram of Puzzle

Two perfect conducting spheres are immersed in a fluid with electrical conductivity σ = 5 x 10-2 S/m. The spheres have radius r = 1 mm and are maintained a distance R = 1 m apart. A potential difference of V = 220 V is maintained between the two spheres. The fluid extends to infinity. Calculate the net current flowing between the spheres. (If you've been paying attention, you've noticed that this situation violates charge continuity. So let the potential difference be maintained by a perfect battery that is connected to the spheres with perfect wires that are insulated from the surrounding fluid. However, you can neglect the volume taken up by the wires and battery.)

This puzzle was inspired by my stove developing a short circuit a few weeks ago.


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