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 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 magnetic field applied to the strip?

Q2:

The density of charge carriers for copper is 8 . 7 4 × 1 0 2 8 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 6 . 0 × 1 0 7 V
  • B 3 . 0 × 1 0 7 V
  • C 7 . 6 × 1 0 7 V
  • D 4 . 7 × 1 0 7 V
  • E 8 . 5 × 1 0 7 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 mm2. The strip is attached to a battery and immersed in a 1.50-T magnetic field aligned perpendicularly to the strip's surface. The battery produces a 2.00-mA electric current through the length of the strip and 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 1 . 3 2 × 1 0 m−3
  • B 1 . 2 5 × 1 0 m−3
  • C 1 . 4 0 × 1 0 m−3
  • D 1 . 5 6 × 1 0 m−3
  • E 1 . 4 9 × 1 0 m−3

Q4:

A strip of copper with a cross-sectional area of 4 . 6 × 1 0 6 m2 is placed in a uniform magnetic field of magnitude 3.11 T. The Hall electric field is measured to be 2 . 5 × 1 0 3 V/ms. In modelling the characteristics of the current in the strip, use a value of 𝑛 = 9 . 2 × 1 0 2 8 electrons/m3 for copper.

What is the drift speed of the conduction electrons?

  • A 0 . 2 × 1 0 4 m/s
  • B 9 . 2 × 1 0 4 m/s
  • C 5 . 5 × 1 0 4 m/s
  • D 8 . 0 × 1 0 4 m/s
  • E 3 . 3 × 1 0 4 m/s

What is the current in the strip?

  • A 54 A
  • B 98 A
  • C 41 A
  • D 32 A
  • E 63 A

What is the Hall coefficient of the strip?

  • A 7 . 6 × 1 0 1 1 C−1
  • B 1 . 3 × 1 0 1 1 C−1
  • C 6 . 8 × 1 0 1 1 C−1
  • D 8 . 5 × 1 0 1 1 C−1
  • E 4 . 2 × 1 0 1 1 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 3 . 9 × 1 0 m3
  • B 7 . 2 × 1 0 m3
  • C 4 . 2 × 1 0 m3
  • D 4 . 7 × 1 0 m3
  • E 5 . 0 × 1 0 m3

Q7:

A velocity selector in a mass spectrometer uses a magnetic field of magnitude 0.127 T. The velocity selector selects a speed of 4 . 6 × 1 0 6 m/s.

What is the required electric field magnitude?

  • A 3 . 3 × 1 0 5 V/m
  • B 8 . 4 × 1 0 5 V/m
  • C 8 . 2 × 1 0 5 V/m
  • D 5 . 8 × 1 0 5 V/m
  • E 6 . 2 × 1 0 5 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 1 . 9 9 × 1 0 3 m3/s
  • B 2 . 6 3 × 1 0 3 m3/s
  • C 2 . 0 5 × 1 0 3 m3/s
  • D 2 . 2 6 × 1 0 3 m3/s
  • E 2 . 8 2 × 1 0 3 m3/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?

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