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

Question

BlackTom AI · Accepted Answer

Coulomb's law states that the magnitude of the electrostatic force between two point charges is proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them.

1. Relevant concepts
- Electrostatic force between point charges.
- Proportionality to charge product and inverse-square dependence on separation.
- Mathematical form: F = k |q1 q2| / r^2, where k = 1/(4πε0) ≈ 8.988×10^9 N·m^2/C^2, and the vector form includes the unit vector r̂ to give direction.

2. Step-by-step reasoning
- The question phrase "directly proportional to the product of charges" corresponds to a factor q1·q2 in the numerator of the law.
- The phrase "inversely proportional to the square of separation between them" corresponds to a division by r^2.
- Combining these gives F ∝ q1 q2 / r^2. Introducing the proportionality constant k yields the complete formula F = k q1 q2 / r^2 (magnitude).
- The sign and direction (attraction if charges opposite, repulsion if same sign) come from the algebraic product q1 q2 and the vector direction r̂.

3. Intermediate/calculation details
- Example constants: k = 1/(4πε0) ≈ 8.988×10^9 N·m^2/C^2.
- If q1 = 1 μC and q2 = 2 μC separated by r = 0.1 m, then F = k*(1e-6*2e-6)/(0.1^2) = 8.988×10^9 * 2e-12 / 1e-2 = 8.988×10^-1 N ≈ 0.8988 N.

4. Why the correct answer is correct
- The exact wording in the question matches the statement of Coulomb's law (product of charges in numerator, r^2 in denominator), so option d is the correct identification.

5. Why other options are incorrect
- a. Gauss’s law relates electric flux through a closed surface to enclosed charge, not the two-charge force formula.
- b. Newton’s law (likely Newton’s law of gravitation) is an inverse-square law for masses, not electric charges; it involves G and masses, not q1q2.
- c. Ohm’s law is V = IR, relating voltage, current, and resistance—unrelated to force between charges.

Conclusion: The correct choice is d. Coulomb's law, which matches the provided answer.

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单项选择题

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