# Current flow between two points

I can measure a voltage that is induced on my skin from a 50hz electromagnetic field (emf) source using a multimeter, how can I measure the induced current flowing between my finger and ground when I touch a grounded wire whilst in the same electromagnetic field.

I have tried using an ammeter to measure the current under the impression that the positive terminal would serve as a ground. However I cannot get a positive reading whilst doing this. My understanding is that current flows from high to low potentials. Why is it that no current registers on the multimeter?

Following ohms law I would expect to see the 1v measured on my skin, which in this model has a resistance of 10,000 ohms, translate to a current of 0.1 milliamp however the multimeter/ammeter doesnt register this. Why not?

You have most likely been measuring a voltage that was induced in the loop formed by the multimeter leads and your skin. Do the measurement again, this time just shorting the leads while forming a loop of similar area. If the voltage is still there, it has nothing to do with your skin.

If you wanted to measure the electrostatic current from your body acting as a capacitive antenna to ground, you would need an electrometer with much higher impedance. Your body capacitance is on the order of 100pF. The $10k\Omega$ internal resistance of your instrument forms a highpass with a frequency of 160kHz with that capacitance. An AC voltage with a frequency of 50Hz will be suppressed by a factor of 3000 by that highpass. Another way of looking at it is that you are actually doing a current measurement with your voltmeter, rather than a voltage measurement.

So what's the AC current flowing trough your body? If the voltage is 230V (the current line voltage in Europe, I believe), then there will be $230V*2\pi*100pF*50Hz=7.2uA$ of current flowing in the best case, which is probably below the sensitivity of your instrument. The good news is that you can easily build your own electrometer amplifier with not much more than a couple batteries and a CMOS opamp these days.

This is a nice circuit that anybody can build with reasonable success: http://amasci.com/electrom/sas51p1.html#Electro. For your purposes you can bypass the filter circuit around the fourth opamp and if all you want is to detect the 50Hz capacitively coupled AC signal, then you won't need OP 2 and 3, either. The simple circuit around OP1 is enough. You can use two 9V batteries as power supply. Put the circuit in a metal box (a food can is perfect!) and make sure that everything is kitchen clean, because modern Opamps can detect sub-pA (some can do fA!) of current and getting an electrometer to behave nicely depends on absolutely cleanliness around the input leads. Even small amounts of solder residue and other organic matter that attracts moisture will short circuit the small currents that you are trying to measure and the circuit will do strange things like drift to one of the rails and do wild voltage swings on its own. On the upside, if you master the design of electrometer amplifiers and you understand what you are doing, then you have learned one of the basic skills of an experimental physicist/EE.

• The voltage is only there when I touch the positive probe, and is not dependent on the configuration of the probe wires. So I am quite sure the multimeters wires are relitively unaffected by induced voltage. Are you suggesting that no current will flow between my skin and ground when in an ac elctromagnetic field?
– SIRT
May 19, 2015 at 1:18
• @SIRT: Are you sure you gave me the right impedance for the multimeter? A modern digital multimeter has an impedance of 1-10MOhm, which is closer to an electrometer than the old style 10kOhm that one would get from a galvanometer style instrument. In that case you would be detecting a capacitively coupled signal, so it's the opposite of the case that I was describing. Of course, even at 10MOhm, you are still looking at a high pass with 160Hz, so you are still not "measuring" the real change in your body's electrostatic potential. There is, of course, a current flow, but it's small. May 19, 2015 at 1:29
• sorry, I don't think I made myself clear. The 10,000 ohms refers to the resistance between two points on my skin.
– SIRT
May 19, 2015 at 1:42
• OK, that makes more sense. So what's the impedance of the multimeter? Is the multimeter battery operated or does it have an AC power supply? The reason why I am asking is because with an AC operated instrument you are now getting into nasty problems of so called "common mode rejection". May 19, 2015 at 1:46
• I'm not sure of the impedance but I do know it's 9v battery operated.
– SIRT
May 19, 2015 at 1:54