To determine which of the alternatives has the strongest electric force acting on a -3 Coulomb charge, we can use Coulomb's Law, which states that the force \( F \) between two point charges is given by the formula:
\[ F = k \frac{|q_1 q_2|}{r^2} \]
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.
Let’s calculate the force for each option based on the formula.
-
An object with a -4 charge at a distance of 2 cm (0.02 m): \[ F = k \frac{|-3 \cdot -4|}{(0.02)^2} = k \frac{12}{0.0004} = k \cdot 30000 \]
-
An object with a -3 charge at a distance of 5 cm (0.05 m): \[ F = k \frac{|-3 \cdot -3|}{(0.05)^2} = k \frac{9}{0.0025} = k \cdot 3600 \]
-
An object with a +3 charge at a distance of 5 cm (0.05 m): \[ F = k \frac{|-3 \cdot 3|}{(0.05)^2} = k \frac{9}{0.0025} = k \cdot 3600 \]
-
An object with a +3 charge at a distance of 2 cm (0.02 m): \[ F = k \frac{|-3 \cdot 3|}{(0.02)^2} = k \frac{9}{0.0004} = k \cdot 22500 \]
Now let's compare the results:
- Option 1: \( k \cdot 30000 \)
- Option 2: \( k \cdot 3600 \)
- Option 3: \( k \cdot 3600 \)
- Option 4: \( k \cdot 22500 \)
From these calculations, we can see that Option 1, with the -4 charge at a distance of 2 cm, results in the strongest force.
Final Answer: An object with a -4 charge at a distance of 2 cm.