The Hall effect can be used to determine the sign of the mobile charges in a particular conducting material. A bar of a new
kind of conducting material is connected to a battery as shown in Figure 21.106. In this diagram, the x axis runs to the right,
the y axis runs up, and the z axis runs out of the page, toward you. A voltmeter is connected across the bar as shown, with
the leads placed directly opposite each other along a vertical line. In order to answer the following questions, you should
draw a careful diagram of the situation, including all relevant charges, electric fields, magnetic fields, and velocities.
Initially, there is no magnetic field in the region of the bar.
(a) Inside the bar, what is the direction of the electric field due to the charges on the batteries and surface of the
wires and the bar? This is the electric field that drives the current in the bar.
(b) If the mobile charges in the bar are positive, in what direction do they move when current runs?
(c) If the mobile charges in the bar are negative, in what direction do they move when current runs?
(d) In this situation (zero magnetic field), what is the sign of the reading on the voltmeter? Now large coils (not shown)
are moved near the bar, and current runs through the coils, making a magnetic field in the direction (into the
page).
(e) If the mobile charges in the bar are negative, what is the direction of the magnetic force on the mobile charges?
(f) If the mobile charges in the bar are negative, which of the following things will happen?
(1) Positive charge will accumulate on the top of the bar.
(2) The bar will not become polarized.
(3) Negative charge will accumulate on the left end of the bar.
(4) Negative charge will accumulate on the top of the bar.
(g) If the mobile charges in the bar are positive, what is the direction of the magnetic force on the mobile charges?
(h) If the mobile charges in the bar are positive, which of these things will happen?
(1) Positive charge will accumulate on the top of the bar.
(2) The bar will not become polarized.
(3) Positive charge will accumulate on the right end of the bar.
(4) Negative charge will accumulate on the top of the bar.
You look at the voltmeter and find that the reading on the meter is volts. What can you conclude from
this observation? (Remember that a voltmeter gives a positive reading if the positive lead is attached to the higher
potential location.)
(1) There is not enough information to figure out the sign of the mobile charges.
(2) The mobile charges are negative.
(3) The mobile charges are positive.