The circuit diagram reveals to us that the time course of the extracellular field potential will be roughly proportional to Im, or:
For electrical events that are relatively fast with respect to the membrane time constant, such as action potentials or fast EPSPs, most of the current exiting at B will be capacity current across CB. For fast conductance changes (∆g fast with respect to tm), the time course of extracellular field potential is proportional to the rate of change (first derivative) of the transmembrane potential, or
Slower events would cause a steady extracellular potential, thus this relation would not be true.
The fact that extracellular field potential has a time course approximately equal to transmembrane current allows us to use our recording to estimate current flow.
Visual Lesson Another way to look at it.