A homopolar generator consists of a metal disk that rotates in the presence of a
ID: 1531516 • Letter: A
Question
A homopolar generator consists of a metal disk that rotates in the presence of a magnetic field perpendicular to the disk's face. Sliding contacts connect the axle and the disk's outer surface to an external circuit. Explain why this device produces a constant potential difference between the two contacts if the disk rotates at a constant rate. Determine the magnitude of the potential difference in terms of the disk's radius R, the magnetic field strength |B vector | and the disk's angular rotation rate omega (in radians per second).Explanation / Answer
a) The metal portions of the apparatus are conducting, and confine a current due to electronic motion to within the metal boundaries. All electrons that move in a magnetic field experience a Lorentz force of
F = qv × B
F=force
v=velocity
electron=q
where v is the velocity of the electrons and q is the charge on an electron. This force is perpendicular to both the velocity of the electrons, which is in the plane of the disc, and to the magnetic field, which is normal (surface normal) to the disc. An electron at rest in the frame of the disc moves circularly with the disc relative to the B-field, and so experiences a radial Lorentz force, this radial force, is the cause of the current.
b) Electrons in a conducting disk in order to maintain equilibrium will have to have a centripetal force on them equal to the local change in potential energy with respect to a change in radius, that is
me2r=ed/dr
After integrating, we get a potential difference between the center and a point R out
= me2 R2/2e
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