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I would like to be able to measure magnetic fields that are generated by nerve impulses in extremities like in fingers. I know that they are very weak: about 100 mV electric potential would give us about current 10 mA if resistance = 1/10 Ohm, but interested in measuring magnetic fields.

How many rounds should you have in a coil to measure 10 mA current?

The jumping of electrons from one level to another may become a problem in this case. However, I am not sure where and how.

Assume that there is a steady current in the situation so Biot-Savart law. The radius of the nerve is r = 0.003m.

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You have a problem with units here, you say you want to measure magnetic fields, but you quote a strength in mV which is a unit of electric potential. – dmckee Nov 12 '12 at 19:29
@dmckee I fixed the confusion. I think the answer should be get by Biot-Savart law when assuming that r = 0.003m. Let's assume that there is a steady current in the situation, probably wrong assumption, but not sure which law to use for not steady currents. – Masi Nov 12 '12 at 20:17
It's possible to measure very weak magnetic fields, indeed: – Jerry Schirmer Nov 12 '12 at 20:26
@JerrySchirmer: you should promote your comment to an answer. I was about to add an answer referring to SQUIDs but it would say little more than your comment. The OP obviously hasn't encountered SQUIDs since he's thinking of using a coil. – John Rennie Nov 13 '12 at 9:38
@JerrySchirmer: I agree with John Rennie. You should promote that into the answer. Just look at the upvotes you got on a Comment (how often are comments upvoted anyway?). – centralcharge Sep 29 '13 at 6:53
up vote -1 down vote accepted

SQUIDs are sensitive enough to measure fields as low as 5 aT (5×10−18 T). So 5 aT is the best one that can be reached at the moment.

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