Cambridge International AS and A level Physics
Exercise 27.3 The Hall effect This exercise develops your understanding of the idea of an electron passing undeviated through a field, and of the formula that involves mean drift velocity. The charge on the electron, e = −1.6 × 10−19 C. 1 Describe what is meant by the Hall effect. 2 A conventional current enters face P of a thin slice of a semiconductor. Only electrons flow in the thin slice. A magnetic field B acts downwards. face R
B
t
d
B
current enters face P
current leaves face Q face S
a State the direction of movement of the electrons as the current enters face P. b Use Fleming’s left-hand rule to find the direction of the magnetic force on the electrons. c Explain which face becomes negatively charged due to the Hall effect. d State where a voltmeter should be connected to measure the Hall voltage. e The equation qE = Bqv is used in explaining the Hall effect. State the meaning of the two terms qE and Bqv. 178
f
Explain why the two terms are equal.
g Show how the equation qE = Bqv is used to derive the expression for VH the Hall voltage, BI given by VH = ntq , where t is the thickness of the slice. You will need to use the electric field
formula for parallel plates and the formula for current in terms of the mean drift velocity of the electrons, as well as recognising that the area A = dt. h The current in the film is 0.042 A, t = 0.9 mm, d = 10 mm, the Hall voltage is 2.0 × 10 −4 V and the concentration of free electrons in the semiconductor is 1.5 × 1023 m−3. Calculate the magnetic field strength, B. i
Calculate the electric field strength in the slice due to the Hall effect voltage.
j
Calculate the mean drift velocity of the electrons.
3 This diagram shows a Hall probe placed near a wire carrying a direct current: Hall probe A
B current in wire
The Hall voltage is +1.6 mV. a State the cause of the magnetic field that produces the Hall voltage in the probe. b Explain why the Hall voltage is zero when the coil rotates 90º about the axis AB from the position shown. c Explain why the Hall voltage is −1.6 mV when the coil rotates 180º about the axis AB from the position shown. d Explain why the Hall voltage decreases when the probe is moved towards B along the line AB.