Site all assumptions (values not given, equations, and physics laws) and NEATLY
ID: 1539368 • Letter: S
Question
Site all assumptions (values not given, equations, and physics laws) and NEATLY show ALL work.
When a magnetic field is applied perpendicular to the current in a conducting wire, a potential Delta V_H called the Hall voltage develops across the conductor perpendicular to both the current and the magnetic field. A metal ribbon is 2.0 mm wide and 0.15 mm thick. It carries a current of 3 A along its length. In a perpendicular magnetic field of 2.0 T, a Hall voltage of 150 mu V is measured across its width. What is the drift velocity of the conduction electrons? The current in a conductor depends on the density of conduction electrons (n), the cross-sectional area of the conductor (A) and the drift velocity: I = neAv_D. Using this relation and your result from part (a), deduce the free electron density of the metal. (This will be a number of electrons per unit volume.)Explanation / Answer
a) Using
Vh = vdwB
Where
Vh is hall's voltage
vd is drift velocity
w is width
B is magnetic field
Substituting values
150*10^-6 = vd*0.15*10^-3*2
vd = 0.5m/s
b) n = I/eAvd
n = 3/1.60*10^-19*2*0.15*10^-6*0.5 = 1.25*10^26 e/m^3