Coulomb's Law states that the magnitude of the electrostatic force between two point charges is:

Question

BlackTom AI · Accepted Answer

Coulomb's law: F = k |q1 q2| / r^2, so the magnitude of the electrostatic force is proportional to the product of the charges and inversely proportional to the square of the distance between them.

1) Relevant knowledge points and concepts
- Coulomb's law: magnitude F = k |q1 q2| / r^2, where k ≈ 8.99×10^9 N·m^2/C^2 in vacuum.
- Proportionality: F ∝ q1 q2 (product), and F ∝ 1/r^2 (inverse-square dependence).
- The law gives magnitude; sign and direction come from charge signs and vector form but do not change the stated proportionalities.

2) Step-by-step reasoning
- Start from the standard formula F = k |q1 q2| / r^2.
- This shows F increases linearly with either charge (if one charge doubles, F doubles), which implies dependence on the product q1 q2.
- The r^2 in the denominator shows the inverse-square law: if distance doubles, force becomes one-quarter.

3) Calculation example with intermediate steps
- Choose q1 = 2 C, q2 = 3 C, r = 4 m for demonstration.
- Compute product: q1 q2 = 2 × 3 = 6 C^2.
- Compute r^2 = 4^2 = 16 m^2.
- Magnitude F = k × 6 / 16 = (6/16) k = 0.375 k ≈ 0.375 × 8.99×10^9 ≈ 3.37×10^9 N.
- This shows explicit use of product and inverse-square dependence.

4) Why the correct answer is correct
- The formula directly matches the wording: "Directly proportional to the product of the charges" (q1 q2) and "inversely proportional to the square of the distance" (1/r^2). That is the precise statement of Coulomb’s law for magnitudes.

5) Why the other options are incorrect
- Any option invoking the sum of charges is wrong because Coulomb’s law depends on the product q1 q2, not q1 + q2.
- Options that state inverse proportionality to distance (1/r) are wrong because the dependence is 1/r^2 (inverse-square), not 1/r.

6) Conclusion
- Therefore the correct choice is: "Directly proportional to the product of the charges and inversely proportional to the square of the distance between them." This matches the provided answer.

Coulomb's Law states that the magnitude of the electrostatic force between two point charges is:单项选择题

类似问题

A charge of 2 X 10-7 C is acted upon by a force of 0.1 N. Determine the distance to the other charge of 4.5 X 10-7 C with both the charges in vacuum.

In a Coulomb’s Law experiment, if the charge of one object is doubled, what would happen to the force on the other charged object?

The law that states that "the force is directly proportional to the product of charges and inversely proportional to the square of separation between them" is called

A charge of 2 X 10-7 C is acted upon by a force of 0.1N. Determine the distance to the other charge of 4.5 X 10-7 C with both the charges in vacuum.

If you are give the relationship 𝐹 = 𝑘 𝑞 2 𝑟 2 + 𝐶 and you plotted 𝐹 vs 1 𝑟 2 which of the following would be true about your graph?

Two point charges are 2 cm apart. They are moved to a new separation of 8 cm. By what factor does the resulting mutual force between them change?

The force between a 30 μC charge and a 90 μC charge is 1.8 N. How far apart are they?

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