Homework SourseA gold wire consists of the three segments shown in the figu
A gold wire consists of the three segments shown in the figure below, in which d = 1.1 mm and D = 2.2 mm. The current I in the top segment is 12 A. What are the following for the top, middle and bottom?
| (a) current I (A) | 12 | ||
| (b) current density J (A/m2) | |||
| (c) electric field E (N/C) | |||
| (d) drift velocity vd (m/s) | |||
| (e) mean time between collisions (s) | |||
| (f) electron current i (s-1) |
Solution
1. current remains the same. current Itop = Imid = Ibot = 12 A
2. current density, Jtop = Jbottom = I/A = 12 /pi*(1.1x10^-3)^2 = 3.158e+6 A/m^2
Jmid = I/A = 12 /pi*(1.1x10^-3/2)^2 = 1.2627e+7 A/m^2
3. electric field: Etop = Ebottom = J / Sigma = 3.158e+6 / 3.5x107 = 0.09 N/C
electric field: Emid = J / Sigma = 1.2627e+7 / 3.5x107 = 0.36 N/C
4. the drift speed is,
vd,top = vd,bottom = J/ne = 3.158e+6 / 6x10^28*1.6x10^-19 = 3.29e-4 m/s
vd,mid= J/ne =1.2627e+7 / 6x10^28*1.6x10^-19 = 1.31e-3 m/s
