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Unformatted text preview: Lab 4: The Classical Hall Effect 1 Introduction Understanding the motion of charge carriers in mag- netic fields has led to several interesting practical ap- plications. The deflection of an electron beam in a magnetic field can be used to measure the charge to mass ratio of electrons and ions. Mass spectrometers that are used to measure the masses of isotopes find widespread applications in archaeology, geology, and planetary science. The period of orbital motion of a charged particle in a uniform magnetic field is inde- pendent of the velocity of the particle. This is the ba- sis for particle accelerators such as cyclotrons. High- energy collisions in particle accelerators and cloud chambers (used for studying cosmic rays) are analyzed by photographing the curved trajectories of charged particles (produced during these collisions) in mag- netic fields. The classical Hall effect (discovered in 1879 by E. H. Hall) is also related to the motion of charge carriers in magnetic fields. It led to some of the earliest ex- periments that established the sign of charge carriers in conductors. It has been used to measure the num- ber density of charge carriers in conductors, as well as the drift velocity of charge carriers in the presence of a uniform electric field in the conductor. Such an electric field can be established by connecting the ter- minals of a battery to the conductor. The classical Hall effect is commonly used in magnetic field sensors that are reliable, accurate, and relatively inexpensive. During this lab, you will carry out some simple ex- periments that will allow you to verify the Hall effect. You will determine the sign of the charge carriers in two kinds of semiconductors. The drift velocity of the charge carriers in the sample and the number of charge carriers per unit volume can also be determined from your data. EXERCISES 1 AND 7 PERTAIN TO THE BACKGROUND CONCEPTS AND EXER- CISES 2-6 AND 8-10 PERTAIN TO THE EX- PERIMENTAL SECTIONS. 2 Background A particle with charge q moving with a velocity-→ v in a uniform magnetic field-→ B will experience a force-→ F ,-→ F = q (-→ v ×-→ B ) (1) Consider the motion of free electrons in a conducting wire at room temperature. In the absence of an elec- tric field, the electrons will move in random directions with a characteristic velocity distribution. The aver- age velocity of the electrons is zero, and their most probable speed is related to the thermal energy of the electrons. This thermal energy is proportional to the temperature of the conductor. If the conductor is con- nected to a battery, the electrons will experience a force due to the electric field-→ E B inside the conduc- tor. The electrons will be accelerated in a direction opposite the field. However, collisions with the lat- tice of ions that make up the wire will dissipate the increase in the kinetic energy of the electrons due to the electric field. As a result, the electrons acquire a drift velocity-→ v d in addition to their random ther-...
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