# Worksheet: Explaining the Hall Effect

In this worksheet, we will practice calculating the Hall voltage across a conductor when a magnetic field is applied perpendicular to the current.

**Q1: **

A thin rectangular strip of semiconductor has a width of 5 cm
and a cross-sectional area of 2 mm^{2}.
The strip is connected to a battery and placed in a magnetic field perpendicular to the surface of the strip.
A Hall voltage of 12.5 V is produced across the strip,
associated with a drift velocity of 50 m/s.
What is the magnitude of the magnetic field applied to the strip?

**Q2: **

The density of charge carriers for copper is electrons per cubic meter. A probe made of a copper plate of length 3.0 cm, width 2.0 cm, and thickness 1.0 cm is placed in magnetic field of 2.5 T, aligned perpendicular to the length-width plane. If a current of 1.5 A is passed through the probe, what Hall voltage value does it measure?

- A V
- B V
- C V
- D V
- E V

**Q3: **

The surface of a thin rectangular strip of a semiconductor has a width of 10.0 cm
and a length of 30.0 cm.
The cross-sectional area of the strip is 1.00 mm^{2}.
The strip is attached to a battery and immersed in a magnetic field of 1.50 T
aligned perpendicularly to
the strip’s surface. The battery produces an electric current of 2.00 mA
through the length of the strip and a Hall voltage
of 12.0 V is produced across the strip’s
width. What is the number density of the charge carriers in the semiconductor?

- A m
^{−3} - B m
^{−3} - C m
^{−3} - D m
^{−3} - E m
^{−3}

**Q4: **

A strip of copper with a cross-sectional area of m^{2} is placed in a uniform magnetic field of magnitude 3.11 T. The Hall electric field is measured to be V/m. In modeling the characteristics of the current in the strip, use a value of electrons/m^{3} for copper.

What is the drift speed of the conduction electrons?

- A m/s
- B m/s
- C m/s
- D m/s
- E m/s

What is the current in the strip?

What is the Hall coefficient of the strip?

- A C
^{−1} - B C
^{−1} - C C
^{−1} - D C
^{−1} - E C
^{−1}

**Q5: **

The Hall voltage measured by a Hall probe for a certain sample is 3.5 µV when a current of 2.7 A and a magnetic field magnitude of 1.2 T is used to generate the Hall voltage. If a current of 2.1 A generates a Hall voltage measurement of 3.0 µV for the same sample, what is the magnitude of the magnetic field?

**Q6: **

The Hall effect was used to find the density of charge carriers in a rectangular sample of an unknown material with length 2.2 cm, width 1.5 cm, and height 0.30 cm. A Hall voltage of 57 µV for a 3.4 A current along the length of the sample was observed in a 3.8 T magnitude magnetic field perpendicular to the current. Determine the density of the charge carriers in the sample.

- A m
^{3} - B m
^{3} - C m
^{3} - D m
^{3} - E m
^{3}

**Q7: **

A velocity selector in a mass spectrometer uses a magnetic field of magnitude 0.127 T. The velocity selector selects a speed of m/s.

What is the required electric field magnitude?

- A V/m
- B V/m
- C V/m
- D V/m
- E V/m

What is the potential difference across the selector’s plates if they are separated by a distance of 1.33 cm?

**Q8: **

To construct a nonmechanical water meter, a magnetic field of magnitude 0.750 T is placed across the supply water pipe to a home, and a Hall voltage of 66.7 mV is recorded for a certain flow rate.

Find the flow rate through a pipe of diameter 3.23 cm.

- A m
^{3}/s - B m
^{3}/s - C m
^{3}/s - D m
^{3}/s - E m
^{3}/s

What would the Hall voltage be through a pipe of diameter 13.0 cm if the flow rate did not change?

**Q9: **

An experiment is performed to demonstrate the Hall effect. A thin rectangular strip of semiconductor with width 15 cm and length 45 cm is attached to a battery and immersed in a 2.25 T magnetic field perpendicular to its surface. This produces a Hall voltage of 16 V. What is the drift velocity of the charge carriers?