Question

The Hall effect can be used to calculate the charge-carrier number density in a conductor. A conductor carrying current of 2.0 A is 0.50 mm thick, and the Hall voltage is 4.5 x 10-6 V when it is in a uniform magnetic field of 1.2 T. What is the density of charge carriers in the conductor? a) n = 4.6 x 1027 charges/m b) n = 1.7 x 1027 charges/m c) n = 1.0 x 1028 charges/m d) n = 6.7 x 1027 charges/m²

Answer 1

Answer:

option D

Explanation:

given,

A conductor is carrying current = 2.0 A is 0.5 mm thick

Hall voltage = 4.5 x 10-6 V

uniform magnetic field  =  1.2 T

density of the charge = n =?

hall voltage =$V_h =\dfrac{i\ B}{n\ e\ L}$

$n = \dfrac{i\ B}{V\ e\ L}$

$n = \dfrac{2 \times 1.2 }{4.5 \times 10^{-6}\times 1.6 \times 10^{-19} \times 0.5 \times 10^{-3}}$

n = 6.67 × 10²⁷ charges/m

hence the correct answer is option D