Consider this very simple and well-known experiment with dirty/salty water:
The light bulb turns on, and current is flowing. How can you know how this current is exactly flowing, and how the electric field looks like through the liquid? Is it a very confined path, or does it spread over the whole electrolyte? How does the conductivity of the fluid affect the shape? Are there other parameters that can tune the shape (e.g., AC frequency if not using a battery, voltage, shape of the wires and wire ends, ...)?