A) A Hall probe serves to measure magnetic field strength. Such a probe consists
ID: 1431456 • Letter: A
Question
A) A Hall probe serves to measure magnetic field strength. Such a probe consists of a poor conductor 0.145 mm thick, whose charge-carrier density is 1.09 × 1025 m–3. When a 1.55-A current flows through the probe, the Hall voltage is measured to be 4.35 mV. What is the magnetic field strength?
B) An electron enters a region of space containing a uniform 0.0000173-T magnetic field. Its speed is 163 m/s and it enters perpendicularly to the field. Under these conditions, the electron undergoes circular motion. Find the radius r of the electron's path, and the frequency f of the motion. radius = _______ ; frequency = _______
Explanation / Answer
(A)
Expression for hall voltage:
VH = I B / n e d
Magnetic field strength:
B = VH n e d / I
= 4.35x10^-3 * 1.09x10^25 * 1.6x10^-19 * 0.145x10^-3 / 1.55
= 0.71 T
(B)
Radius of the path:
r = m v / q B
= 9.11x10^-31 * 163 / (1.6x10^-19 * 0.0000173 )
= 5.36x10^-5 m
Time period:
T = 2 pi r / v
Frequency:
f = 1 / T
= v / 2 pi r
= 163 / ( 2 pi * 5.36x10^-5 )
= 4.8x10^5 Hz
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