Solution:The law of physics that states that the force between the two electric charges reduces to a quarter of its former value when the distance between them is doubled is Coulomb's Law.
Coulomb's Law states that the electrostatic force between two point charges is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between their centers. Mathematically, it is expressed as:
where:
- (F) is the electrostatic force between the charges.
- (k) is Coulomb's constant.
- (q_1) and (q_2) are the magnitudes of the charges.
- (r) is the distance between the centers of the two charges.
^2}=k\frac{|q_1&space;q_2|}{4r^2}=\frac{1}{4}\left(k\frac{|q_1&space;q_2|}{r^2}\right)=\frac{1}{4}F&space;)
This shows that when the distance between the two electric charges is doubled, the force between them reduces to one-quarter (a quarter) of its original value. This inverse square relationship is a key feature of Coulomb's Law.