While walking along a sidewalk, the back of my hand brushed the guardrail. There was a stinging sensation like an ant bite or maybe I had hit a sharp spot on the metal. Curious, I stopped to check and not seeing any bugs or a mark on the back of my finger, I reached down to gently feel the metal for sharp spots and..... zap! - there it was again.  This felt more like a small electrical shock. I found that if I made firm contact with the rail, there was no sensation whatsoever, but if I let my hand lightly brush the surface of the metal, I would get a definite shock. I realized I was standing beneath high voltage power transmission lines and it all made sense - sort of. Obviously, the lines were inducing a sufficient voltage into the guardrail to give me a minor shock. But on further reflection, it didn't make sense. The guardrail was bolted to steel "I" beams driven into the ground so the guardrail had to be very close to ground potential. Also, I was wearing rubber soled sneakers so I was insulated from ground. It wasn't plausible that the guardrail could be at sufficient potential above ground to force a sensible current through my shoes, to the concrete sidewalk. It must be the other way around - the lines were charging the surface of my body to a sufficient voltage that when I touched the grounded guardrail..... zap! Not harmful - extremely low current - no sensation at all when I firmly touched the metal.

So how much voltage? I got a digital voltmeter and returned to the site. I held one probe between my fingers and touched the other to the guardrail at intervals as I approached the overhead lines. Two hundred feet away 0.1 volts. One hundred feet 0.3 volts. Seventy five feet 1 volt. Fifty feet 10 volts and it kept going up as I got closer! I estimate the lines are 30 to 35 feet above the sidewalk. The highest voltage I measured was about 730 volts between me and the guardrail! This is across a voltmeter with a 10 Megohm input resistance so the current was 73 micro-amps. This was at a position just off to either side of the lines. When I was centered directly below the lines the voltage was much lower - about 250 volts. This makes sense since the lines are elements of a balanced 3 phase system. If I could stand at a point exactly the same distance from each of the 3 lines then the potential between my body and ground would be zero (assuming identical line to line voltages - a condition that is satisfied in practical power transmission systems). The line to line voltage for this particular transmission line is about 230 kV giving a line to ground voltage of about 133 kV.

Each phase produces a voltage gradient. The voltage on my body is proportional to the vectorial total gradient at a point centered in the space I occupy. I wanted a graph that would show how the voltage on my body would change based on my position on the ground. The gradient contribution of each phase to me is proportional to the phase voltage and inversely proportional to my distance from the line. The total gradient is proportional to the vectorial sum of the contribution of each phase. The exact gradient value is not required.  I produced a very simple numerical model based on the forgoing that generated the graph below. The diagram shows the key distances used in the model. I used 4 meters for S, 10 meters for H, and 1 meter for B. D was varied from -20 meters to +20 meters where 0 is directly under phase B. The resulting curve correlates well with measurements I made at different positions along the guard rail. Notice that the field maximums are off to the sides of the A and C phase lines (not directly under them) and reaches a local minimum directly under B phase. I also measured the potential difference across my body from forehead to ankle of about 30 volts.