Introductory Physics Volume Two

88 Magnetic Fields 4.6
both easily measured.
The Hall effect also allows us to determine if the charge carriers
are positive or negative. In the analysis above we assumed that the
charge carriers were negatively charged electrons. Consider what would
happen if the charge carriers were positive instead. The positive charges
would also be deflected by the magnetic field.
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+
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Which will build up a field in the opposite direction.
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+ + + + + + + + + + + + + + + + + + +
E E E E E
- - - - - - - - - - - - - - - - - - -
Thus we can determine from the sign of the Hall voltage, if the charge
carriers are positive or negative. There are some types of semiconductors
that have positive charge carriers, for example silicon with a little
bit of aluminum mixed in. Semiconductors with positive charge carriers
are called p-type semiconductors. Semiconductors with negative
charge carriers are called n-type semiconductors.
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§ 4.6 More Examples
Example
An electron is injected horizontally into a parallel plate capacitor with
a velocity v = 4 × 10 6 m s : A, +Q
-e
v
A, -Q
The plates are square, with sides 20cm and the charge on the capacitor
is 7.5µC. Describe what magnetic field is required such that the net
force on the electron is zero between the capacitor plates. Ignore any
edge effects.
The electric field points down, since the top plate on the capacitor is
positive. However, since the electron has a negative charge, the electric
force is up. Thus, the force caused by the magnetic field must be down.
Here is what the force diagram on the electron must look like