Question

The mean time between collisions for electrons in room temperature copper is 2.5 x 10-14 s. What is the electron current in a 2 mm diameter copper wire where the internal electric field strength is 0.01 V/m?

Answer 1

1.87 A

Step-by-step explanation:

τ = mean time between collisions for electrons = 2.5 x 10⁻¹⁴ s

d = diameter of copper wire = 2 mm = 2 x 10⁻³ m

Area of cross-section of copper wire is given as

A = (0.25) πd²

A = (0.25) (3.14) (2 x 10⁻³)²

A = 3.14 x 10⁻⁶ m²

E = magnitude of electric field = 0.01 V/m

e = magnitude of charge on electron = 1.6 x 10⁻¹⁹ C

m = mass of electron = 9.1 x 10⁻³¹ kg

n = number density of free electrons in copper = 8.47 x 10²² cm⁻³ = 8.47 x 10²⁸ m⁻³

`i` = magnitude of current

magnitude of current is given as

`i = (Ane^(2)\tau E)/(m)`

`i = ((3.14* 10^(-6))(8.47* 10^(28))(1.6* 10^(-19))^(2)(2.5* 10^(-14)) (0.01))/((9.1* 10^(-31)))`

`i` = 1.87 A