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 D
Interaction D

Interaction A
Interaction A

Interaction C

1 answer

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

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

where:

  • \( F \) is the force,
  • \( k \) is Coulomb's constant,
  • \( q_1 \) and \( q_2 \) are the magnitudes of the charges,
  • \( r \) is the distance between the charges.

We need to calculate the force for each interaction:

Interaction A:

  • Charge 1 = +2
  • Charge 2 = -2
  • Distance = 1 \[ F_A = k \frac{|2 \times -2|}{1^2} = k \frac{4}{1} = 4k \]

Interaction B:

  • Charge 1 = +1
  • Charge 2 = -1
  • Distance = 1 \[ F_B = k \frac{|1 \times -1|}{1^2} = k \frac{1}{1} = 1k \]

Interaction C:

  • Charge 1 = +2
  • Charge 2 = -2
  • Distance = 4 \[ F_C = k \frac{|2 \times -2|}{4^2} = k \frac{4}{16} = \frac{1}{4}k \]

Interaction D:

  • Charge 1 = +1
  • Charge 2 = -1
  • Distance = 4 \[ F_D = k \frac{|1 \times -1|}{4^2} = k \frac{1}{16} = \frac{1}{16}k \]

Now, we can summarize the calculations:

  • \( F_A = 4k \)
  • \( F_B = 1k \)
  • \( F_C = \frac{1}{4}k \)
  • \( F_D = \frac{1}{16}k \)

From the computed forces, we see that the force is strongest in Interaction A.

Therefore, the correct answer is:

Interaction A