Two charged objects separated by some distance attract each other If the charges on both objects are doubled with no change in distance between them. what happens to the magnitude of the force between the objects? The force between them remains unchanged The force between them is quartered The force between them also doubles The force between them quadruples The force between them is halved

## Step 1:<br />The problem involves the concept of Coulomb's Law, which states that the force between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. This relationship is mathematically represented as:<br /><br />### \( F = k \cdot \frac{|q1 \cdot q2|}{r^2} \)<br /><br />where \( F \) is the force, \( k \) is Coulomb's constant, \( q1 \) and \( q2 \) are the charges, and \( r \) is the distance between the charges.<br /><br />## Step 2:<br />In this problem, the charges on both objects are doubled, but the distance between them remains the same. Therefore, the new force \( F' \) can be calculated by substituting \( 2q1 \) and \( 2q2 \) into the formula:<br /><br />### \( F' = k \cdot \frac{|2q1 \cdot 2q2|}{r^2} = 4 \cdot k \cdot \frac{|q1 \cdot q2|}{r^2} = 4F \)<br /><br />This shows that the new force is four times the original force.