Section 4.1 · Worked examples · 2 of 4
Worked example 4.1.2: Hall voltage in a copper strip
About the worked examples of Section 4.1
Four short calculations tied to the applications. They use only , its wire form and the long-wire field of Problem 4.1.1, with no new physics. Constants used: H/m ( H/m) and C. A good way to use them: read the given quantities, produce the formula from the Lorentz force or from Problem 4.1.1 yourself, and only then put the numbers in.
Hall voltage in a copper strip
#cf. Application 4.1.1
Given. A copper strip, mm wide, μm thick, carries A in T normal to its face. Copper: m, .
Find. (a) current density and drift speed, (b) Hall field and Hall voltage, (c) the same strip in doped InSb, m.
The carriers drift along the strip with . Each feels across the width. Charge piles up on the two long edges until the transverse (Hall) field balances it, . The Hall voltage is , and with one gets , Eq. (4.1.23).
A/m A/mm. With C/m,
The transverse field balances :
Directly: μV, the same.
The readouts reproduce mm/s and μV. Choose InSb for part (c).
and : the same , and would give times more, about V, which is why Hall elements are made of semiconductors and run at a few milliamperes.
Electrons crawl at a fraction of a millimetre per second, yet a lamp lights at once when the switch closes: it is the field that travels along the wire, not the carriers. The sign of tells which edge is positive and hence the sign of the carriers, and gives . In copper the carriers are electrons: they move against , and with both and reversed pushes them to the same edge a positive carrier would reach, so the edge polarity is reversed.