Taking into account the geometry of the Hall effect in the metal lamina we can
write:
|
(96) |
EH = -v-× B = B × v- |
|
(97) |
tgθH=EH=- Vt b ii |
|
(98) |
θH= arctgknB |
where
|
(99) |
kn=- E- |
kn is called electron mobility in the metal lamina. If we suppose that the electric
polarizing field EH is constant the electric voltage VH between M’ and M is:
|
(100) |
—7 —7 VH = EHh = V-× B ■ sinα ■ h |
where α is the angle between the vectors B and V- (if α=90o then sinα=1). The
condition EH = const is fulfilled if V- = const and B = const. The current density
J- through the surface S of the lamina is:
|
(101) |
7 i_ J = — = V en -S - |
|
(102) |
V-= RHJ- |
|
(103) |
RH = -1 H en |
where n denotes the number of the elementary charges e in unity volume, and
RH is called Hall resistance. RH can thus be measured to find the density of
carriers in the material.
56
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