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.
A thin rectangular strip of semiconductor has a width of 5 cm and a cross-sectional area of 2 mm2. 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?
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
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 mm2. 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
A strip of copper with a cross-sectional area of m2 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/m3 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
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?
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 m3
- B m3
- C m3
- D m3
- E m3
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?
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 m3/s
- B m3/s
- C m3/s
- D m3/s
- E m3/s
What would the Hall voltage be through a pipe of diameter 13.0 cm if the flow rate did not change?
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?