I'm a physicist taking a class on cell biology and we are currently discussing the concept of an electrochemical gradient, the difference in potential (voltage) and chemical concentrations across a membrane. My instructor stated that a neurons resting potential is caused by these two opposing "forces" reaching an equilibrium across a membrane that is permeable to potassium ions, but essentially impermeable to sodium ions.
The electrical gradient is quite straightforward. More positive charge on one side of a membrane would create a net coulombic force towards the other side. Chemical gradient, on the other hand, is not governed by any technical "force." Instead, diffusion down chemical gradients is simply a consequence of entropy, and can be described using Fick's Law.
It is unclear to me how diffusion can in any way oppose electrical force. Allow me to demonstrate this with two thought experiments using a container full of water that is divided in two halves using a membrane that is permeable only to potassium ions. In the first experiment, 10 potassium ions are dropped onto one side of the container. After some time, the potassium ions would have passively diffused across the membrane and, on average, each side of the membrane would have 5 potassium ions at any given moment. In the second experiment, rather than being empty, the other half of the container has 10 (or more!) sodium ions. As the potassium ions begin to diffuse toward the membrane, they would feel the force from the ten (or more) positive sodium ions and, on average, stay on their side of the container. This proves that the chemical gradient cannot oppose an electrical gradient.