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Two point charges each experience a 1 N electrostatic force when they are 2 cm apart. If they are moved to a new separation of 8 cm, what is the magnitude of the electric force on each of them?
A
4 N
B
0.25 N
C
1 N
D
0.5 N
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1
Understand that the problem involves Coulomb's Law, which describes the electrostatic force between two point charges. The formula is: , where is the force, is Coulomb's constant, are the charges, and is the separation distance.
Recognize that the initial force is 1 N when the charges are 2 cm apart. This gives us a reference point to use Coulomb's Law to find the product of the charges .
Set up the ratio of forces using Coulomb's Law for the two different distances. Since the force is inversely proportional to the square of the distance, we have: = , where is the new distance.
Substitute the known values into the ratio: = , where is the new force.
Solve for the new force using the ratio: = . This will give you the magnitude of the electric force at the new separation distance.