Question

Which of the following models has the greatest attractive electric force between the charged particles?
+1|———10mm ————十1

+1 |——- 10mm ————| -1

+1 |—- 5mm ——| -1

+1 |—- 5mm ——| +1

Answer 1

To determine which of the configurations has the greatest attractive electric force between the charged particles, we can apply Coulomb's Law, which states that the electric force \( F \) between two point charges is given by:

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

where:
- \( F \) is the magnitude of the force,
- \( k \) is Coulomb's constant (\( 8.99 \times 10^9 \, \text{N m}^2/\text{C}^2 \)),
- \( q_1 \) and \( q_2 \) are the magnitudes of the charges,
- \( r \) is the distance between the charges.

We need to analyze each of the configurations:

1. **Configuration 1:**
- Charges: \( +1 \, \text{C} \) and \( -1 \, \text{C} \)
- Distance \( r = 10 \, \text{mm} = 0.01 \, \text{m} \)
- Force \( F = k \frac{|-1 \times 1|}{(0.01)^2} \)

2. **Configuration 2:**
- Charges: \( +1 \, \text{C} \) and \( -1 \, \text{C} \)
- Distance \( r = 10 \, \text{mm} = 0.01 \, \text{m} \)
- Force \( F = k \frac{|-1 \times 1|}{(0.01)^2} \) (This is the same as Configuration 1)

3. **Configuration 3:**
- Charges: \( +1 \, \text{C} \) and \( -1 \, \text{C} \)
- Distance \( r = 5 \, \text{mm} = 0.005 \, \text{m} \)
- Force \( F = k \frac{|-1 \times 1|}{(0.005)^2} \)

4. **Configuration 4:**
- Charges: \( +1 \, \text{C} \) and \( +1 \, \text{C} \)
- Distance \( r = 5 \, \text{mm} = 0.005 \, \text{m} \)
- This is a repulsive force, as both charges are positive.

Now, let’s evaluate the forces where they are attractive (Configurations 1, 2, and 3).

- For Configurations 1 and 2 (10 mm distance):
\[
F_1 = k \frac{1}{(0.01)^2} = k \times 10^4
\]

- For Configuration 3 (5 mm distance):
\[
F_3 = k \frac{1}{(0.005)^2} = k \times 4 \times 10^4
\]

Since \( F_3 \) (from Configuration 3) is \( 4 \) times the force of Configurations 1 and 2, we can conclude that:

**Configuration 3 has the greatest attractive electric force between the charged particles.**