In the context of non-contact forces and electric charges, the relationship between the charges on objects and the electric force between them can be explained as follows:
The electric force between two objects is determined by their electric charges according to Coulomb's Law. This law states that:
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Like Charges Repel: When two objects have the same type of charge (both positive or both negative), they repel each other. This results in a force pushing them apart.
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Opposite Charges Attract: When one object has a positive charge and the other has a negative charge, they attract each other. This results in a force pulling them together.
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Magnitude of Force: The strength of the electric force between two charged objects is proportional to the product of the magnitudes of their charges and inversely proportional to the square of the distance between them. Mathematically, this can be represented by the equation:
\[ F = k \frac{{|q_1 q_2|}}{{r^2}} \]
where \( F \) is the magnitude of the electric force, \( k \) is Coulomb's constant, \( q_1 \) and \( q_2 \) are the magnitudes of the charges, and \( r \) is the distance between the centers of the two charges.
In summary, the charges on objects dictate the nature and strength of the electric force between them: like charges repel, opposite charges attract, and the magnitude of the force depends on the amount of charge and the distance between the objects.