Your roommate is sold on magnet therapy, a sham treatment using small bar magnet

Question

Your roommate is sold on magnet therapy, a sham treatment using small bar magnets attached to the body. You skeptically ask your roommate how this is supposed to work. He mumbles something about the Hall effect speeding blood flow. In reply, you estimate the Hall potential associated with typical blood parameters in the 100-G field of a bar magnet: red blood cells carrying 2- pC charge in a 12-cm flow through a 3.0-mm -diameter blood vessel containing 5 billion red blood cells per mL . To show that the Hall potential is negligible, you compare your estimate with the tens of mV typical of bioelectric activity. How do the two values compare?

Explanation / Answer

The Hall voltage is determined by balancing the Lorentz force on a charge with the electrostatic force field that arises when the charges are pulled to one side: q v B = q E q v B = q V/d V = d v B with d = 3.0 *10^-3 m, v = 0.12 m/s and B = 1.00* 10^-2 T this gives V_H = 3.6 * 10^-5 Volts, i.e. 36 microvolt

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