Figure 32.1: The Hall effect. (Ref. [13])If the two currentsI 1 andI 2 are in thesamedirection, the wires willattract; if the currents are in the
oppositedirection, the wires willrepel. (This is in a sense “backwards” from the rule you might expect, based
on the rules the force between two electric charges or two magnetic poles—but this is the way it works out.)
Eq. (32.6) is used in the definition of the ampere: 1 ampere is defined to be that current which, when
passed through each of two long parallel wires 1 meter apart, gives a force per unit length of 2 10 ^7
newtons per meter, as can be verified by substitutingI 1 DI 2 D 1 A anddD 1 m into Eq. (32.6).
32.4 The Hall Effect
Suppose we run an electric current though a wire—say the current runs from right to left. Such a current
could be due topositivecharges moving from right to left, or tonegativecharges moving left to right. How
can we tell the actual charge of the carriers of electric current?
An experiment to determine the correct charge of the carriers of electric current was performed in 1895
at the Johns Hopkins University by Edwin H. Hall. If an electric current is run through a conducting strip
in a magnetic field, then opposite sides of the strip will acquire opposite electric charge, and therefore a
potential difference will be created across the strip. Thedirectionof this potential difference will be different,
depending on whether the current is carried by positive or negative charges. This phenomenon is called the
Hall effect.
The principle of the experiment is shown in Figure 26.1. The positive end of a battery is connected to
the right end of the strip, and the negative end to the left end; a magnetic field is directed into the page. If
the current is carried bypositivecharges moving right to left, then the Lorentz force on the positive charge
will cause the positive charges carrying the current to move downward toward the bottom of the strip, and the
electric field due to these charges will pointupward.
If, on the other hand, the current is carried bynegativecharges moving left to right, then the Lorentz
force on the negative charges will cause the negative charges carrying the current to also move downward,
toward the bottom of the strip. In this case the electric field due to the charges carrying the current will point
downward.
When Hall performed his experiment in 1895, he discovered that the latter situation is what actually
occurs: the electric field across the strip points downward, so that the carriers of the electric current must
benegative. This experiment was done in 1895—the yearbeforethe discovery of the electron by British