Which, among the following is the correct expression for an electric field?

Question

BlackTom AI · Accepted Answer

Electric field E is defined as the force experienced per unit positive test charge, so E = F / q (vector relationship: E = F/q).

1) Relevant knowledge points and concepts
- Electric field (E) is a property of space around charges that exerts a force F on a test charge q: E ≡ F/q.  
- Coulomb’s law for the force between two point charges q (source) and Q (test) is F = k q Q / r^2.  
- Units: force F in newtons (N), charge q in coulombs (C), so E has units N/C (equivalently V/m).  
- Direction: E points in the direction of the force on a positive test charge.

2) Complete reasoning step by step
- Start with Coulomb’s law: F = k q Q / r^2 (force on test charge Q due to source q).  
- Divide both sides by Q to get the field at that point: F / Q = (k q Q / r^2) / Q.  
- Cancel Q: (k q Q / r^2) / Q = k q / r^2.  
- Thus E = F / Q = k q / r^2, showing E is independent of the test charge magnitude.

3) Intermediate calculation steps (shown above)
- F = k q Q / r^2
- E = F/Q = (k q Q / r^2) / Q = k q / r^2

4) Why the correct answer is correct
- E = F/Q matches the definition of electric field (force per unit charge) and yields correct units (N/C). It also reduces properly to the familiar expression from Coulomb’s law.

5) Why the other options are incorrect
- b. E = F * Q multiplies force by charge, giving units N·C and no physical meaning for the field.  
- c. E = F * C uses capacitance (C) or charge symbol ambiguously and multiplies — incorrect units and unrelated concept.  
- d. E = F / C divides force by capacitance (F/C with F meaning force), producing N/Farad which is not N/C and is physically meaningless for electric field.

6) Conclusion
The correct expression is E = F/Q, which matches option a. Confirmed: a. E=F/Q.

Which, among the following is the correct expression for an electric field?单项选择题

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