Question

How does distance affect the force between charged particles?

Answer 1

The force between charged particles, such as electrons and protons, is described by Coulomb's law. Coulomb's law states that the force between two charged particles is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. Mathematically, it can be expressed as:


=

⋅
∣

1
⋅

2
∣

2
F=
r
2
k⋅∣q
1
    ​

⋅q
2
    ​

∣
    ​


Where:


F is the magnitude of the electrostatic force between the charges.

k is Coulomb's constant (
8.9875
×
1
0
9
 
N
⋅
m
2
/
C
2
8.9875×10
9
N⋅m
2
/C
2
 in vacuum).

1
q
1
    ​

 and

2
q
2
    ​

 are the magnitudes of the charges.

r is the distance between the centers of the charges.

As the distance between the charges increases:

The force decreases: Since the force is inversely proportional to the square of the distance, as

r increases,

2
r
2
 increases more rapidly, causing the force to decrease.
The force becomes weaker rapidly: The weakening of the force with distance is not linear, but exponential due to the square in the denominator of the formula. This means that even a small increase in distance can result in a significant decrease in force.

In practical terms, this behavior is similar to how gravity works. Just as objects feel a weaker gravitational pull as they move farther apart, charged particles experience a weaker electrostatic force as they are separated by greater distances.

In summary, distance has a substantial impact on the force between charged particles. The force decreases rapidly as the distance between the charges increases, following the inverse square law described by Coulomb's law.