Question

Question
In which of the following interactions will the amount of force between the two objects be the strongest?

Interaction Charge on Object 1 Charge on Object 2 Distance Between Objects
A +2 -2 1
B +1 -1 1
C +2 -2 4
D +1 -1 4
(1 point)
Responses

Interaction B
Interaction B

Interaction C
Interaction C

Interaction A
Interaction A

Interaction D

Answer 1

To determine which interaction has the strongest force between the two charged objects, we can use Coulomb's Law, which states that the force \( F \) between two point charges is proportional to the product of the magnitudes of their charges and inversely proportional to the square of the distance between them. The formula is:

\[
F = k \frac{|q_1 \cdot q_2|}{r^2}
\]

where:
- \( F \) is the force between the charges,
- \( k \) is Coulomb's constant,
- \( q_1 \) and \( q_2 \) are the charges of the two objects,
- \( r \) is the distance between the charges.

Let's analyze each interaction:

1. **Interaction A:**
- Charge on Object 1: +2
- Charge on Object 2: -2
- Distance: 1
- Force: \( F_A = k \frac{|(+2)(-2)|}{1^2} = k \frac{4}{1} = 4k \)

2. **Interaction B:**
- Charge on Object 1: +1
- Charge on Object 2: -1
- Distance: 1
- Force: \( F_B = k \frac{|(+1)(-1)|}{1^2} = k \frac{1}{1} = 1k \)

3. **Interaction C:**
- Charge on Object 1: +2
- Charge on Object 2: -2
- Distance: 4
- Force: \( F_C = k \frac{|(+2)(-2)|}{4^2} = k \frac{4}{16} = 0.25k \)

4. **Interaction D:**
- Charge on Object 1: +1
- Charge on Object 2: -1
- Distance: 4
- Force: \( F_D = k \frac{|(+1)(-1)|}{4^2} = k \frac{1}{16} = 0.0625k \)

Now we can compare the forces calculated:

- \( F_A = 4k \)
- \( F_B = 1k \)
- \( F_C = 0.25k \)
- \( F_D = 0.0625k \)

The strongest force occurs in **Interaction A**, with a force of \( 4k \).

So the correct answer is:
**Interaction A**