To determine which interaction has the strongest force between the two objects, we can apply Coulomb's Law, which states that the force (F) between two charged objects is proportional to the product of the magnitudes of their charges (q1 and q2) and inversely proportional to the square of the distance (r) between them. The formula is given by:
\[ F = k \frac{|q_1 \cdot q_2|}{r^2} \]
Where:
- \( F \) is the force,
- \( k \) is Coulomb's constant,
- \( q_1 \) and \( q_2 \) are the charges on the two objects,
- \( r \) is the distance between the charges.
Let's analyze each interaction:
-
Interaction A:
- Charges: +2 and -2
- Distance: 1
- Force: \[ F_A = k \frac{|2 \cdot (-2)|}{1^2} = k \frac{4}{1} = 4k \]
-
Interaction B:
- Charges: +1 and -1
- Distance: 1
- Force: \[ F_B = k \frac{|1 \cdot (-1)|}{1^2} = k \frac{1}{1} = 1k \]
-
Interaction C:
- Charges: +2 and -2
- Distance: 4
- Force: \[ F_C = k \frac{|2 \cdot (-2)|}{4^2} = k \frac{4}{16} = \frac{1}{4}k \]
-
Interaction D:
- Charges: +1 and -1
- Distance: 4
- Force: \[ F_D = k \frac{|1 \cdot (-1)|}{4^2} = k \frac{1}{16} = \frac{1}{16}k \]
Now, we compare the forces calculated:
- \( F_A = 4k \)
- \( F_B = 1k \)
- \( F_C = \frac{1}{4}k \)
- \( F_D = \frac{1}{16}k \)
The strongest force is found in Interaction A with \( F_A = 4k \).
Therefore, the correct response is:
Interaction A