To determine the force between the two charged pitch balls, we can use Coulomb's Law, which describes the electrostatic force between two point charges. The formula is given by:
Coulomb's Law
The equation for Coulomb's Law is:
F = k * |q1 * q2| / r²
Where:
- F is the force between the charges.
- k is Coulomb's constant, approximately 8.99 × 10^9 N m²/C².
- q1 and q2 are the magnitudes of the charges.
- r is the distance between the centers of the two charges.
Given Values
In this scenario:
- Mass of each ball, m = 1 g = 0.001 kg (though mass is not needed for calculating the electrostatic force).
- Charge of each ball, q1 = q2 = 1 mC = 1 × 10^-3 C.
- Distance between the charges, r = 1 m (length of the silk thread).
Calculating the Force
Now, substituting the values into Coulomb's Law:
F = (8.99 × 10^9 N m²/C²) * |(1 × 10^-3 C) * (1 × 10^-3 C)| / (1 m)²
Calculating the numerator:
F = (8.99 × 10^9) * (1 × 10^-6) / 1
F = 8.99 × 10^3 N
Now, converting this to a more manageable form:
F = 8.99 × 10^3 N = 8.99 × 10^6 μN
Final Result
Since we need to express the force in terms of micro-Newtons (μN), we can convert:
F = 8.99 × 10^6 μN
However, this value does not match any of the options provided. Let's double-check the calculations and the units:
It appears that the initial charge values and the distance were correctly applied. The force calculated is significantly larger than the options given, indicating a potential misunderstanding in the problem setup or the values provided.
In conclusion, based on the calculations using Coulomb's Law, the force between the two charged pitch balls is approximately 8.99 × 10^6 μN, which does not correspond to any of the answer choices listed. If you have further details or constraints regarding the problem, please share them for a more accurate assessment.
