Object A and object B are initially uncharged and are separated by a distance of 1 meter. Suppose 10,000 electrons are removed from object A and placed on object B, creating an attractive force between A and B. An additional 10,000 electrons are removed from A and placed on B and the objects are moved so that the distance between them increases to 2 meters. By what factor does the electric force between them change?
Assuming that we can treat to both objects, once charged, as point charges, the attractive force between them, must obey Coulomb's Law.
The charge on each object is just the charge of 10,000 electrons:
Q = e*10⁴ = 1.6*10⁻19C*10⁴ = 1.6*10⁻¹⁵ C
As the same charge that we remove from one object in magnitude is the same as the one built on the other, this force can be expressed as follows (in magnitude):
[tex]F =\frac{k*(10e4e)^{2} }{1m}[/tex]
If we increase the charge removing additional 10,000 electrons from A and placed on B, as this incremental charge is equal to the existing charge, this means that the charge on each object will double.
If, at the same time, we double the distance between charges, the force between them can be written as follows:
