To determine the force rankings, we use Coulomb's Law:
[tex]\[ F = k \frac{|Q_1 Q_2|}{r^2} \][/tex]
where [tex]\( F \)[/tex] is the force between two charges, [tex]\( k \)[/tex] is Coulomb's constant, [tex]\( Q_1 \)[/tex] and [tex]\( Q_2 \)[/tex] are the charges, and [tex]\( r \)[/tex] is the separation distance between the charges.
Given that the separation distance and Coulomb's constant are the same for all trials, we can compare the forces based on the product of the charges [tex]\( Q_1 Q_2 \)[/tex] only:
For Trial 1:
[tex]\[ Q_1 = 10 \times 10^{-6} \, C \][/tex]
[tex]\[ Q_2 = 400 \times 10^{-6} \, C \][/tex]
[tex]\[ F_{\text{Trial 1}} \propto |Q_1 \cdot Q_2| = (10 \times 10^{-6}) \cdot (400 \times 10^{-6}) = 4000 \times 10^{-12} = 4 \times 10^{-9} \][/tex]
For Trial 2:
[tex]\[ Q_1 = 5 \times 10^{-6} \, C \][/tex]
[tex]\[ Q_2 = 400 \times 10^{-6} \, C \][/tex]
[tex]\[ F_{\text{Trial 2}} \propto |Q_1 \cdot Q_2| = (5 \times 10^{-6}) \cdot (400 \times 10^{-6}) = 2000 \times 10^{-12} = 2 \times 10^{-9} \][/tex]
For Trial 3:
[tex]\[ Q_1 = 10 \times 10^{-6} \, C \][/tex]
[tex]\[ Q_2 = 600 \times 10^{-6} \, C \][/tex]
[tex]\[ F_{\text{Trial 3}} \propto |Q_1 \cdot Q_2| = (10 \times 10^{-6}) \cdot (600 \times 10^{-6}) = 6000 \times 10^{-12} = 6 \times 10^{-9} \][/tex]
Now, let's compare the values:
- [tex]\( F_{\text{Trial 3}} = 6 \times 10^{-9} \)[/tex] (strongest)
- [tex]\( F_{\text{Trial 1}} = 4 \times 10^{-9} \)[/tex]
- [tex]\( F_{\text{Trial 2}} = 2 \times 10^{-9} \)[/tex] (weakest)
Thus, according to the force magnitudes:
- The strongest force is in Trial 3
- The intermediate force is in Trial 1
- The weakest force is in Trial 2
Therefore, the correct ranking consistent with Anna's data is:
F. Strongest force: Trial 3, Weakest force: Trial 2
