For a charge Q1, the effect of charge Q2 on Q1 will be

Question

BlackTom AI · Accepted Answer

Coulomb's law states the electrostatic force between two point charges q1 and q2 separated by distance r is F = k q1 q2 / r^2 along the line joining them. Newton’s third law requires every force has an equal and opposite reaction, so the force on each charge by the other must be equal in magnitude and opposite in direction.

1) Relevant knowledge points and concepts
- Coulomb’s law: magnitude F = k |q1 q2| / r^2, direction along the line joining charges (attractive for opposite signs, repulsive for like signs).
- Vector form: F12 = k q1 q2 / r^2 r̂12, where r̂12 is the unit vector from charge 1 to charge 2.
- Newton’s third law: F on 1 by 2 = −(F on 2 by 1).

2) Step-by-step reasoning
- Write the force on Q1 due to Q2: F1 = k q1 q2 / r^2 r̂12.
- Write the force on Q2 due to Q1: F2 = k q1 q2 / r^2 r̂21.
- Note r̂21 = −r̂12 because the unit vectors point in opposite directions.

3) Calculations and intermediate steps
- F1 = k q1 q2 / r^2 r̂12.
- Since r̂21 = −r̂12, F2 = k q1 q2 / r^2 (−r̂12) = −(k q1 q2 / r^2 r̂12) = −F1.

4) Why the correct answer is correct
- The algebra above directly shows F2 = −F1: equal magnitude k|q1 q2|/r^2 and opposite direction. This satisfies both Coulomb’s law and Newton’s third law.

5) Why other options are incorrect
- b. “F1 and F2 are not equal”: incorrect because magnitudes are equal by Coulomb’s law.
- c. “F1 = F2 = 0”: only true in special cases (q1 or q2 = 0 or r → ∞), not generally true.
- d. “F1 = F2” (interpreted as equal vectors): incorrect because vectors are opposite in direction; magnitudes equal but signs differ, so F1 ≠ F2 as vectors.

6) Conclusion
The correct choice is a. F1 = −F2, which matches the provided answer.

For a charge Q1, the effect of charge Q2 on Q1 will be单项选择题

类似问题

A neutral object is

A rod with an unknown charge attracts a plastic ball. Which of the following is possible?

Lightning results from electrical charge differences ____.

Which one is the correct statement regarding the directions of the electric forces?

In the Coulomb’s Law formula, what do the symbols F, q, and r, mean respectively?

Which one indicates the correct interactions between different charges and neutral object?

Which one indicates the correct interactions between different charges?

A negative charge is released from rest in a region between two plates of opposite sign. Which one is correct?

更多留学生实用工具

智能学习助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单