According to Coulomb's Law, the electrostatic force FFF between two charged particles with charges q1q_1q1 and q2q_2q2 separated by a distance rrr is given by:
F=k∣q1q2∣r2F=k\frac{|q_1q_2|}{r^2}F=kr2∣q1q2∣
where kkk is Coulomb's constant. If the distance rrr between the two charged particles is halved, the new distance becomes r/2r/2r/2. Substituting this into the formula gives:
F′=k∣q1q2∣(r/2)2=k∣q1q2∣r2/4=4×k∣q1q2∣r2=4FF'=k\frac{|q_1q_2|}{(r/2)^2}=k\frac{|q_1q_2|}{r^2/4}=4\times k\frac{|q_1q_2|}{r^2}=4FF′=k(r/2)2∣q1q2∣=kr2/4∣q1q2∣=4×kr2∣q1q2∣=4F
This means the force between the two charged particles becomes four times greater when the distance between them is halved
Summary:
- Force is inversely proportional to the square of the distance.
- Halving the distance increases the force by a factor of 444.
- Thus, the force becomes four times the original force.
This inverse square relationship is a fundamental characteristic of Coulomb's law and is similar to the behavior of gravitational forces but with much stronger magnitude for charges
