A Hall probe is designed to operate with a steady current of 0.020 A in a semiconductor slice of thickness 0.05 mm. The number density of charge carriers (electrons) in the semiconductor is 1.5 × 10²³ m⁻³.

a. Calculate the Hall voltage that will result when the probe is placed at right angles to a magnetic field of flux density 0.10 T. (Elementary charge e = 1.60 × 10⁻¹⁹ C.)

b. Explain why the current in the Hall probe must be maintained at a constant value.