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)

Interaction C

Interaction A

Interaction B

Interaction D

Answer 1

To determine which interaction has the strongest force between the two objects, we can use Coulomb's law, which states that the force \( F \) between two charged objects is given by the formula:

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

where:
- \( F \) is the magnitude of the force between the charges,
- \( k \) is a constant,
- \( q_1 \) and \( q_2 \) are the magnitudes of the charges,
- \( r \) is the distance between the charges.

Now let's evaluate each interaction:

**Interaction A**
- Charges: +2 and -2, Distance: 1
\[
F_A = k \frac{|2 \cdot -2|}{1^2} = k \frac{4}{1} = 4k
\]

**Interaction B**
- Charges: +1 and -1, Distance: 1
\[
F_B = k \frac{|1 \cdot -1|}{1^2} = k \frac{1}{1} = 1k
\]

**Interaction C**
- Charges: +2 and -2, Distance: 4
\[
F_C = k \frac{|2 \cdot -2|}{4^2} = k \frac{4}{16} = \frac{1}{4}k
\]

**Interaction D**
- Charges: +1 and -1, Distance: 4
\[
F_D = k \frac{|1 \cdot -1|}{4^2} = k \frac{1}{16} = \frac{1}{16}k
\]

Now comparing the magnitudes of the forces:
- \( F_A = 4k \)
- \( F_B = 1k \)
- \( F_C = \frac{1}{4}k \)
- \( F_D = \frac{1}{16}k \)

The strongest force is in **Interaction A** \( (4k) \).

Thus, the answer is **Interaction A**.