To determine which object would have the strongest attraction to an object with a charge of -3 Coulombs, we should use Coulomb's Law, which states that the force between two charges is proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them. The formula is:
\[ F = k \frac{|q_1 \cdot q_2|}{r^2} \]
Where:
- \( F \) is the force between the charges,
- \( k \) is Coulomb's constant,
- \( |q_1| \) and \( |q_2| \) are the magnitudes of the charges, and
- \( r \) is the distance between the charges.
Considering the options given:
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An object with a +3 Coulombs charge at a distance of 5 cm: \[ F \propto \frac{|-3| \cdot |+3|}{(0.05)^2} = \frac{9}{0.0025} \]
-
An object with a -3 Coulombs charge at a distance of 5 cm: (no attraction, since both charges are the same) \[ F = 0 \]
-
An object with a -4 Coulombs charge at a distance of 2 cm: \[ F \propto \frac{|-3| \cdot |-4|}{(0.02)^2} = \frac{12}{0.0004} \]
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An object with a +3 Coulombs charge at a distance of 2 cm: \[ F \propto \frac{|-3| \cdot |+3|}{(0.02)^2} = \frac{9}{0.0004} \]
Now, we can compare the forces:
- For the +3 charge at 5 cm: \( \frac{9}{0.0025} = 3600 \)
- For the -4 charge at 2 cm: \( \frac{12}{0.0004} = 30000 \)
- For the +3 charge at 2 cm: \( \frac{9}{0.0004} = 22500 \)
The strongest attraction will be from the object with the -4 Coulombs charge at a distance of 2 cm, as the force calculated is the highest.
Therefore, the answer is: An object with a -4 charge at a distance of 2 cm.