CIE A Level Physics复习笔记20.1.6 Hall Voltage

Hall Voltage

  • The Hall voltage is a product of the Hall effect
  • Hall voltage is defined as:

The potential difference produced across an electrical conductor when an external magnetic field is applied perpendicular to the current through the conductor

  • When an external magnetic field is applied perpendicular to the direction of current through a conductor, the electrons experience a magnetic force
  • This makes them drift to one side of the conductor, where they all gather and becomes more negatively charged
  • This leaves the opposite side deficient of electrons, or positively charged
  • There is now a potential difference across the conductor
    • This is called the Hall Voltage, VH

Hall Voltage, downloadable AS & A Level Physics revision notes

The positive and negative charges drift to opposite ends of the conductor producing a hall voltage when a magnetic field is applied

  • An equation for the Hall voltage VH is derived from the electric and magnetic forces on the charges

20.1-Hall-voltage-derivation-diagram

The electric and magnetic forces on the electrons are equal and opposite

  • The voltage arises from the electrons accumulating on one side of the conductor slice
  • As a result, an electric field is set up between the two opposite sides
  • The two sides can be treated like oppositely charged parallel plates, where the electric field strength E is equal to:

8.-Hall-Voltage-equation-1

  • Where:
    • VH = Hall voltage (V)
    • d = width of the conductor slice (m)
  • A single electron has a drift velocity of v within the conductor. The magnetic field is into the plane of the page, therefore the electron has a magnetic force Fto the right:

FB = Bqv

  • This is equal to the electric force FE to the left:

FE = qE

qE = Bqv

  • Substituting E and cancelling the charge q

8.-Hall-Voltage-equation-2

  • Recall that current I is related to the drift velocity v by the equation:

I = nAvq

  • Where:
    • A = cross-sectional area of the conductor (m2)
    • n = number density of electrons (m-3)
  • Rearranging this for v and substituting it into the equation gives:

8.-Hall-Voltage-equation-3

  • The cross-sectional area A of the slice is the product of the width and thickness t:

A = dt

  • Substituting A and rearranging for the Hall voltage VH leads to the equation:

8.-Hall-Voltage-equation-48.-Hall-Voltage-equation-5

  • Where:
    • B = magnetic flux density (T)
    • q = charge of the electron (C)
    • I = current (A)
    • n = number density of electrons (m-3)
    • t = thickness of the conductor (m)
  • This equation shows that the smaller the electron density n of a material, the larger the magnitude of the Hall voltage
    • This is why a semiconducting material is often used for a Hall probe
  • Note: if the electrons were placed by positive charge carriers, the negative and positive charges would still deflect in opposite directions
    • This means there would be no change in the polarity (direction) of the Hall voltage

Exam Tip

Remember to use Fleming’s left-hand rule to obtain the direction the electrons move due to the magnetic force created by the magnetic field.

 

 

 

 

 

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