(a) A long straight rod with cross sectional area A and conductivity accelerates parallel to its...

(a) A long straight rod with cross sectional area A and conductivity σ accelerates parallel to its length with acceleration a. Write down the Drude-like equation of motion for the average velocity v of an electron of mass m in the rod relative to the motion of the rod itself. Show that, in the absence of an external electric field, there is a steady solution that corresponds to a current I = Aσma/e flowing in the wire. Assume that a flexible, no-loss wire and a perfect ammeter close the circuit.
(b) Argue that this result generalizes to an EMF for the case of electrons in an accelerated closed circuit. Ignore the Drude drag force.

(c) Use the results of part (b) to show that a circular wire ring rotated with angular acceleration  carries a  current

where R is the total resistance of the wire and S is the area of the wire circle. Estimate the magnitude of this current for a copper ring of radius 1 cm and cross sectional area 1 mm² which oscillates harmonically around the ring axis at 500 Hz, with a maximum angular amplitude of 1◦ of arc.

Transcribed Image Text:

E = dl. (ma/e)