Calculate the electric field strength when a force of 4.0 × 10-9 𝑁 acts on a charge of 8.5 × 10-6𝐶.

Question

BlackTom AI · Accepted Answer

Electric field E is defined by E = F / q (force per unit charge), so use that relation directly.

1) Relevant knowledge points and concepts
- Electric field strength E (in N C^-1 or V m^-1) equals the force F (in newtons) experienced by a test charge divided by the magnitude of that charge q (in coulombs): E = F/q.
- Keep track of scientific notation and significant figures: F = 4.0 × 10^-9 N (2 s.f.), q = 8.5 × 10^-6 C (2 s.f.), so the final value should be reported to about 2 significant figures.

2) Complete reasoning process step by step
- Start with E = F / q.
- Substitute the given values: E = (4.0 × 10^-9 N) / (8.5 × 10^-6 C).

3) Calculations with intermediate steps
- Compute the numerical ratio: 4.0 / 8.5 = 0.470588...
- Combine the powers of ten: 10^-9 / 10^-6 = 10^{-9 - (-6)} = 10^{-3}.
- Multiply: 0.470588... × 10^{-3} = 4.70588... × 10^{-4}.
- Round to two significant figures (consistent with the given data): 4.7 × 10^-4 N C^-1.

4) Why the correct answer is correct
- The algebra and exponent manipulation follow directly from E = F/q; the numeric division gives 4.70588×10^-4, which rounds appropriately to 4.7×10^-4 N C^-1. Units are consistent (N/C).

5) Why the other options are incorrect
- a. 4.4 × 10^-4 N C^-1 is too low compared with the exact division (4.70588×10^-4).
- c. 3.4 × 10^-4 N C^-1 is markedly lower and inconsistent with the computed ratio.
- d. 4.12 × 10^-4 N C^-1 is lower than the exact result and does not match correct rounding.

6) Conclusion
- The calculated electric field is 4.7 × 10^-4 N C^-1, which matches the provided correct answer (option b).

Calculate the electric field strength when a force of 4.0 × 10-9 𝑁 acts on a charge of 8.5 × 10-6𝐶.单项选择题

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