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 43µT (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?

This problem seems to me to be another form of the Hall Effect. Basically, at static magnetic field has an electric current going through it which creates a transverse electric field.

In this case, the flow of charge in the river is the electric current. The river has charges because of dissolved salts like magnesium salts, sodium chloride, etc.

In this case, we care about the magnetic field component which points into the earth. The force on an ion (assuming +1 charge) is given by the Lorentz force:

Fmagnetic= evB where v=velocity of the river, B= magnetic field pointing into the earth, e=charge of electron or ion if its valence is +1.

A net charge of positive charges forms on one plate and negative charges form on the other plate because of this Lorentz force.  As these charges build up, an electric field is formed between the plates which counteract the Lorentz force.  When equilibrium is reached, Felectric=Fmagnetic and no more charges are attracted to the plates by the Lorentz force any more.

eE=evB

E=Electric field=Hall Voltage/width of river=V/w

Solving for v, v=V/wB=(1.9*10^-3V)/(300m*43*10^-6T*sin(71 degrees))=0.16m/s

Posted by gregg on 2006-10-21 20:19:52