Final answer:
The magnitude of the maximum electric force between two electrons 27.0 mm apart can be found using Coulomb's law, which yields approximately 6.04 x 10⁻²⁴ N, a value not listed among the provided answer choices.
Step-by-step explanation:
The student's question relates to finding the magnitude of the maximum electric force exerted by two electrons when they are 27.0 mm apart. To determine this, we can use Coulomb's law, which states that the electrostatic force (F) between two point charges (q₁ and q₂) is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance (r) between them:
F = k * |q₁ * q₂| / r²
Where:
- k is the Coulomb's constant (8.9875 x 10⁹ N･m²/C²)
- q₁ and q₂ are the charges of the electrons (-1.602 x 10⁻¹⁹ C each)
- r is the separation distance (27.0 mm, or 0.027 m)
To calculate the force, we apply these values to Coulomb's law:
F = (8.9875 x 10⁹ N･m²/C²) * |(-1.602 x 10⁻¹⁹ C) * (-1.602 x 10⁻¹⁹ C)| / (0.027 m)²
After calculations, we find that F ≈ 6.04 x 10⁻²⁴ N,
Hence, none of the provided answer choices (A. 3.2×10⁻²⁷ N, B. 1.2×10¹⁰ N, C. 3.2×10⁻²⁵ N, D. 1.2 N) are correct.