If 3.0 × 1015 electrons flow through a section of a wire of diameter 2.0 mm in 4.0 s, what is the current in the wire? (e = 1.60 × 10−19 C)

Question

BlackTom AI · Accepted Answer

Current is total charge per time: I = Q / t, with Q = (number of electrons) × (elementary charge). Use magnitude of charge here.

1) Relevant concepts
- Charge carried by N electrons: Q = N × e (e = 1.60 × 10^−19 C).
- Electric current magnitude: I = Q / t.
- The wire diameter is irrelevant to this calculation because we are given the number of electrons passing per time (not current density or drift velocity).

2) Step-by-step calculation
- Number of electrons: N = 3.0 × 10^15
- Elementary charge magnitude: e = 1.60 × 10^−19 C
- Total charge: Q = N × e = (3.0 × 10^15) × (1.60 × 10^−19) C
  = (3.0 × 1.60) × 10^(15 − 19) C
  = 4.8 × 10^(−4) C
- Time interval: t = 4.0 s
- Current: I = Q / t = (4.8 × 10^(−4) C) / (4.0 s)
  = 1.2 × 10^(−4) A

3) Unit conversion
- 1 mA = 1.0 × 10^(−3) A, so
  I = 1.2 × 10^(−4) A = 0.12 × 10^(−3) A = 0.12 mA

4) Why the correct answer is correct
The calculation directly follows I = Q/t with the given N and e; arithmetic and exponent handling produce 1.2 × 10^(−4) A, which equals 0.12 mA.

5) Why the other choices are incorrect
- 0.24 mA would be twice the correct value (would result if either N were doubled or t were halved).
- 7.5 × 10^7 A and 7.5 × 10^14 A are many orders of magnitude too large and result from major arithmetic/exponent errors (e.g., treating e incorrectly or not combining powers of ten properly).

Conclusion: The current in the wire is 0.12 mA, which matches the provided correct answer.

If 3.0 × 1015 electrons flow through a section of a wire of diameter 2.0 mm in 4.0 s, what is the current in the wire? (e = 1.60 × 10−19 C)单项选择题

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