High School
SAT
ACT
University
MCAT
LSAT
DAT
Wize University Physics Textbook (Master) > Magnetic Fields and Magnetic Force

The Hall Effect

Velocity SelectorsPrevious Section
Magnetic Force on Current-Carrying WiresNext Section
Popular Courses
Find My Course
0:00 / 0:00

The Hall Effect


The motion of electrons inside conductors is affected by external magnetic fields. This effect is called the Hall effect and can be used to develop sensors that measure the strength of magnetic fields.

Experimental setup

  • Consider an experiment with the following properties:
  • Rectangular slab of conducting material
  • External magnetic field points out of the page
  • Current pointing to the right; that is, positive charges are moving to the right with speed vv and charge qq

  • The magnetic force (F⃗=qv⃗×B⃗\vec F = q\vec v \times \vec B) in this case points downward by the right-hand rule.
  • As a result, the charge accumulates on one edge of the conductor, and charge separation is achieved.
Wize Tip
In conductors, it's actually electrons that are moving, but positive current is used as a convention. This does not change the direction of our magnetic force - if both the charge and the velocity direction were swapped, the force still points down the page.

PAGE BREAK

Results

  • Because the charges are separated, there is an electric field across the conductor, EHE_H.
  • This electric field builds up until the electric force cancels out the magnetic force:
Felec=FmagqEH=qvBEH=vBv=EHB\begin{aligned} F_{elec}&=F_{mag} \\ qE_H&=qvB \\ E_H&=vB \\ \end{aligned}\\ \boxed{v = \frac{E_H}{B}}
  • This is the speed of electrons moving in the material.
  • There is also a potential difference across the conductor:
ΔVH=EHdΔVH=vBd\begin{aligned} \Delta V_H &= E_H d \\ \Delta V_H &= vB d \\ \end{aligned}

Practice: The Hall Effect


To measure the magnetic field strength of a solenoid, you place a piece of copper wire inside it. The wire has a square cross-sectional area with side lengths of 2.0 cm and the copper wire is able to detect a Hall voltage.

If you measure a current of 0.20 A across the piece of copper, what is the magnetic field strength inside of the solenoid if the measured Hall voltage is 3.0 nanoVolts?

The density of free electrons in copper is 8.48×10288.48\times10^{28} electrons per cubic meter. Enter your answer with two sig figs in units of Tesla.