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Faraday's experiment (Posted on 2006-10-20) Difficulty: 3 of 5
January 12th in 1832 Michael Faraday did the following experiment in London:

He placed two copperplates in the Thames river at opposite ends of a bridge crossing at 300m apart. He then connected these copperplates with insulated wires to a voltage meter.
He measured a 19mV voltage. Magnetic field in London is measured to be 43ÁT (43*10^-6 T) and inclination is 71 degrees.

Why did Faraday's meter measure a voltage and what was the velocity of the water in the river Thames at that time?

No Solution Yet Submitted by atheron    
Rating: 4.0000 (1 votes)

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Solution Solution and thoughts | Comment 7 of 9 |
Once I looked up how magnetometers work, and one of the ways is called the Hall effect.  Basically, a current is run through a metal plate, and the voltage is measured between the two ends of the plate.

This river experiment is pretty much the same, except the river is technically not a current, since positive and negative charges are moving in the same direction.

Time for those ever-useful equations I learned in E&M:

F = qv x B = |qv|*|B|*sin(θ)
E = ∫F dx = qvBsin(θ)*L
E = ∫q dV
qV = qvBcos(θ)*L
v = V/(Bcos(θ)*L) = .019 V / (43*10^-6 T * sin(71║) * 300 m )
v = 1.56 m/s

This disagrees with gregg's answer by a factor of ten, but this is only because he input 1.9 mV rather than 19.

Qualitatively, what is happening here is that positive ions are on average tending toward one side of the river, while negative ions are tending towards the other side of the river.  There are plenty of these ions in river water, and even in distilled water there is about 10^-7 M concentration of hydrogen and hydroxide ions.  As a result of the ion migration, there is an electrostatic force causing a voltage. 

Other thoughts:

One may ask: why don't the electrostatic force and magnetic force cancel out to create zero voltage?  I think it is because the copper plates themselves are not moving with respect to the magnetic field like the river is.

Another question is: what would happen if the river did not have sufficient ions to cause electrostatic force?  What if rather than a river of water, it was a river of some other, less ionizable substance?  Or maybe a river of something completely neutral like neutrons or neutrinos?  When does the voltage disappear?

And since it was mentioned in previous comments, I think that the magnetic poles rotate with the earth--they are not changing throughout the day.  The pole is somewhere over Canada right now, and it migrates slightly over the years.  However, the magnetic field does fluctuate slightly through the day as a result of the solar wind--but not enough on the earth's surface to affect this experiment.

  Posted by Tristan on 2006-10-22 22:48:18
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