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  • Describe the Hall effect.
  • Calculate the Hall emf across a current-carrying conductor.

We have seen effects of a magnetic field on free-moving charges. The magnetic field also affects charges moving in a conductor. One result is the Hall effect, which has important implications and applications.

[link] shows what happens to charges moving through a conductor in a magnetic field. The field is perpendicular to the electron drift velocity and to the width of the conductor. Note that conventional current is to the right in both parts of the figure. In part (a), electrons carry the current and move to the left. In part (b), positive charges carry the current and move to the right. Moving electrons feel a magnetic force toward one side of the conductor, leaving a net positive charge on the other side. This separation of charge creates a voltage ε size 12{ε} {} , known as the Hall emf    , across the conductor. The creation of a voltage across a current-carrying conductor by a magnetic field is known as the Hall effect    , after Edwin Hall, the American physicist who discovered it in 1879.

Figure a shows an electron with velocity v moving toward the left. The magnetic field B is oriented out of the page. The current I is running toward the right. The force vector on the electron points downward. An illustration of the right hand rule shows the right thumb pointing left with the v vector, the fingers pointing toward 7 o’clock with the B vector, the force vector on a positive charge pointing up and the force vector on a negative charge pointing down. Figure b shows a positive charge moving toward the right. The magnetic field lines are coming out of the page. The current I is running toward the right. The force on the positive charge is down. An illustration of the right hand rule shows the thumb pointing in the direction of the charge’s velocity, the fingers pointing in the direction of B, and F pointing down away from the palm.
The Hall effect. (a) Electrons move to the left in this flat conductor (conventional current to the right). The magnetic field is directly out of the page, represented by circled dots; it exerts a force on the moving charges, causing a voltage ε , the Hall emf, across the conductor. (b) Positive charges moving to the right (conventional current also to the right) are moved to the side, producing a Hall emf of the opposite sign, –ε . Thus, if the direction of the field and current are known, the sign of the charge carriers can be determined from the Hall effect.

One very important use of the Hall effect is to determine whether positive or negative charges carries the current. Note that in [link] (b), where positive charges carry the current, the Hall emf has the sign opposite to when negative charges carry the current. Historically, the Hall effect was used to show that electrons carry current in metals and it also shows that positive charges carry current in some semiconductors. The Hall effect is used today as a research tool to probe the movement of charges, their drift velocities and densities, and so on, in materials. In 1980, it was discovered that the Hall effect is quantized, an example of quantum behavior in a macroscopic object.

The Hall effect has other uses that range from the determination of blood flow rate to precision measurement of magnetic field strength. To examine these quantitatively, we need an expression for the Hall emf, ε size 12{ε} {} , across a conductor. Consider the balance of forces on a moving charge in a situation where B size 12{B} {} , v size 12{v} {} , and l size 12{l} {} are mutually perpendicular, such as shown in [link] . Although the magnetic force moves negative charges to one side, they cannot build up without limit. The electric field caused by their separation opposes the magnetic force, F = qvB size 12{F= ital "qvB"} {} , and the electric force, F e = qE size 12{F rSub { size 8{e} } = ital "qE"} {} , eventually grows to equal it. That is,

qE = qvB size 12{ ital "qE"= ital "qvB"} {}

or

E = vB . size 12{E= ital "vB"} {}

Note that the electric field E size 12{E} {} is uniform across the conductor because the magnetic field B size 12{B} {} is uniform, as is the conductor. For a uniform electric field, the relationship between electric field and voltage is E = ε / l size 12{E=ε/l} {} , where l size 12{l} {} is the width of the conductor and ε size 12{ε} {} is the Hall emf. Entering this into the last expression gives

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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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