Copper contains 8.4×1028 free electrons/m3 . A copper wire of cross-sectional area 7.4×10−7 m 2carries a current of 1 A. The electron drift speed is approximately:A. 3 × 108 m/sB. 103 m/sC. 1 m/sD. 10−4 m/sE. 10−23 m/s
Question
Copper contains 8.4×1028 free electrons/m3 . A copper wire of cross-sectional area 7.4×10−7 m 2carries a current of 1 A. The electron drift speed is approximately:A. 3 × 108 m/sB. 103 m/sC. 1 m/sD. 10−4 m/sE. 10−23 m/s
Solution
The drift speed (v) of electrons can be calculated using the formula:
I = nAvq
where: I = current (in amperes) n = number of free electrons per unit volume (in m^-3) A = cross-sectional area of the wire (in m^2) v = drift speed (in m/s) q = charge of an electron (in coulombs)
Given: I = 1 A n = 8.4×10^28 m^-3 A = 7.4×10^-7 m^2 q = 1.6×10^-19 C (charge of an electron)
We can rearrange the formula to solve for v:
v = I / (nAq)
Substituting the given values:
v = 1 / [(8.4×10^28) * (7.4×10^-7) * (1.6×10^-19)] v = 1 / (9.984×10^10) v = 1.0016×10^-11 m/s
This value is closest to option D (10^-4 m/s), so the answer is D.
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