Question

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

Interaction Charge Charge Distance
Object
1
on object
Between Objects

+2
-2

B
+1
-1
1
C
러
-2
4
D
+1
-1
4
(1 point)
O Interaction D
O Interaction B
• Interaction A
• Interaction C

Answer 1

The force between two charged objects can be determined using Coulomb's Law, which states that the magnitude of the force \(F\) between two point charges 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 amounts of the charges, and
- \(r\) is the distance between the charges.

We must examine each interaction.

**Interaction A:**
- Charges: +2 and -2
- Distance: (not provided; will assume distance is 1 for calculation)
- Force: \(F_A = k \frac{|2 \cdot -2|}{1^2} = k \cdot 4\)

**Interaction B:**
- Charges: +1 and -1
- Distance: 1
- Force: \(F_B = k \frac{|1 \cdot -1|}{1^2} = k \cdot 1\)

**Interaction C:**
- Charges: +1 and -2
- Distance: 4
- Force: \(F_C = k \frac{|1 \cdot -2|}{4^2} = k \cdot \frac{2}{16} = k \cdot \frac{1}{8}\)

**Interaction D:**
- Charges: +1 and -1
- Distance: 4
- Force: \(F_D = k \frac{|1 \cdot -1|}{4^2} = k \cdot \frac{1}{16}\)

Now, let's compare the forces:

- \(F_A \text{ (force from Interaction A)} = k \cdot 4\)
- \(F_B \text{ (force from Interaction B)} = k \cdot 1\)
- \(F_C \text{ (force from Interaction C)} = k \cdot \frac{1}{8}\)
- \(F_D \text{ (force from Interaction D)} = k \cdot \frac{1}{16}\)

Based on the calculations, **Interaction A** has the strongest force: \(F_A = k \cdot 4\).

Thus, the answer is:
• Interaction A