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:
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Configuration 1:
- Charges: \( +1 , \text{C} \) and \( -1 , \text{C} \)
- Distance \( r = 10 , \text{mm} = 0.01 , \text{m} \)
- Force \( F = k \frac{|-1 \times 1|}{(0.01)^2} \)
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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)
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Configuration 3:
- Charges: \( +1 , \text{C} \) and \( -1 , \text{C} \)
- Distance \( r = 5 , \text{mm} = 0.005 , \text{m} \)
- Force \( F = k \frac{|-1 \times 1|}{(0.005)^2} \)
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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).
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For Configurations 1 and 2 (10 mm distance): \[ F_1 = k \frac{1}{(0.01)^2} = k \times 10^4 \]
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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.
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