Answer to Question #146810 in Electricity and Magnetism for Besmallah Yousefi

Question

Hall effect: Describe the Hall effect with the aid of a neat, labeled diagram. What is the significance of the Hall effect, how can it be used to characterise metals and semiconductor? Show that the Hall voltage, V_H, is given by V_H= (v_D)Bw, where w is the width of the wafer of material, (v_D) is the drift velocity of the charge carriers and B the perpendicular magnetic flux density.

Answer 1

Hall effect is the production of a voltage difference across an electrical conductor, transverse to an electric current in the conductor and to an applied magnetic field perpendicular to the current.

When a beam of charged passes through a magnetic field, force act on the particles and the bean is deflected from a straight path. The flow of electrons through a conductor form a beam of charged carriers. When a conductor is placed in a magnetic field proportional to direction of electrons, they will be deflected from a straight path. So, one plane of conductor becomes negatively charged and opposite plane becomes positively charged. The voltage between these planes is called Hall voltage.

Hall effect sensor may operate as an electric switch.

Lorenz force:

F = q(E +vB)

v = v_x = drift velocity

In steady state F = 0

0 = E_y – v_xB_z

Ey = vxBz

In wires electrons are flowing

v_x → -v_x

q → -q

$E_y = \frac{-V_H}{w}$

V_H = v_xB_zw