We examine metal lamina in which under the action of electric field Ei there is
current i- from electrons with mean velocity 1- = const. We have constant
magnetic field with induction B = const, whose lines are perpendicular to the
metal lamina. The vector of velocity v- is collinear with the vector of the electron
current i- . The vectors i- and B define electrodynamic field Emd by:
—7 —7
(92) Emd = v × B
The electromagnetic force FM , which acts upon N moving electrons, is:
(93) Fm = eNv- × B
The electromagnetic force FM has the opposite direction of Emd , thus the side M
is polarized negatively, while M’ is polarized positively. Between M’ and M there
is excited potential electric field with intensity EH . The vector EH has the
opposite direction of Emd . The respective force FH is defined as:
7 7
(94) FH= eNEH
is the opposite of FM . The polarization between M’ and M is over when the two
forces FM and FH get equal. The current is still flowing but the vector J- and the
resultant field E are no more collinear, instead they form the Hall angle θH . Then
the Ohm’s law J- = γE is not valid (γ is the specific conductivity of the metal).
The calculation of θH is simpler when we have monotype current carriers (in our
case electrons). If we have equilibrium
7 7
(95) FM+FH=0.
55
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