When an action potential is induced on a neuron, the local transmembrane potential jumps from $E_{\mbox{rest}}$, the resting potential of the neuron, to $E_{\mbox{eq}}$, the equilibrium potential of an ion or group of ions in the vicinty. Current thus travels in and out of a part of the neuron's cell membrane as ions are exchanged during an action potential. This effect repeats itself as the neighboring regions of the membrane are depolarized, causing the action potential to propagate along the neuron's axon.
Take $\Delta Q$ to be the total charge exchanged locally during an action potential, $C$ to be the membrane capacitance, and $\Delta t$ to be the duration of the action potential. While we can approximate the local average current through an neuron's membrane by taking $$I = \frac{\Delta Q}{\Delta t} = C\frac{\Delta V}{\Delta t} = C\frac{E_{\mbox{eq}} - E_{\mbox{rest}}}{\Delta t}$$ Is there a way to approximate current traveling along the axon of the neuron? Is there even such a thing?