Question

Which pair of objects will have the weakest electric force?
Pair
Object 1 Charge
Object 2 Charge
Distance between Objects (mm)
A
-1
-2
1
B
-2
-2
1
C
+2
+2
3
D
+1
+1
3
(1 point)
Pair A
Pair C
Pair D
Pair B

Answer 1

The electric force between two charged objects can be calculated using Coulomb's law:

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

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

Let's evaluate the pairs in the question:

1. **Pair A: Charges -1 and -2 (1 mm distance)**
\[
F_A = k \frac{|-1 \cdot -2|}{1^2} = k \frac{2}{1} = 2k
\]

2. **Pair B: Charges -2 and -2 (1 mm distance)**
\[
F_B = k \frac{|-2 \cdot -2|}{1^2} = k \frac{4}{1} = 4k
\]

3. **Pair C: Charges +2 and +2 (3 mm distance)**
\[
F_C = k \frac{|2 \cdot 2|}{3^2} = k \frac{4}{9} \approx 0.444k
\]

4. **Pair D: Charges +1 and +1 (3 mm distance)**
\[
F_D = k \frac{|1 \cdot 1|}{3^2} = k \frac{1}{9} \approx 0.111k
\]

Now, we will compare the magnitudes of the forces:
- \( F_A = 2k \)
- \( F_B = 4k \)
- \( F_C \approx 0.444k \)
- \( F_D \approx 0.111k \)

Based on this analysis, the pair with the weakest electric force is Pair D, with a force of approximately \( 0.111k \).

**Answer: Pair D**