the force between two point charge is F in air .what will be the force between them if the distance between becomes double

When considering the force between two point charges, we can refer to Coulomb's Law, which states that the force \( F \) between two charges is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them. The formula is given by:

Coulomb's Law

The mathematical expression for Coulomb's Law is:

F = k * (|q1 * q2|) / r²

Here, \( F \) is the force between the charges, \( k \) is Coulomb's constant, \( q1 \) and \( q2 \) are the magnitudes of the two charges, and \( r \) is the distance between them.

Understanding the Effect of Distance

Now, if the distance \( r \) between the two charges is doubled, we can analyze how this affects the force. Let's denote the original distance as \( r \) and the new distance as \( 2r \). Plugging this into the formula gives:

F' = k * (|q1 * q2|) / (2r)²

When we simplify this, we find:

F' = k * (|q1 * q2|) / (4r²)

Comparing the Forces

From the original force \( F \), we know:

F = k * (|q1 * q2|) / r²

Now, if we compare \( F' \) with \( F \):

F' = F / 4

This means that when the distance between the two point charges is doubled, the new force \( F' \) becomes one-fourth of the original force \( F \).

Real-World Analogy

To visualize this concept, think of two magnets. If you hold them close together, they attract each other strongly. However, if you move them further apart, the attraction weakens significantly. Doubling the distance between the magnets results in a much weaker force, similar to what happens with electric charges.

Summary

In summary, if the distance between two point charges is doubled, the force between them decreases to one-fourth of its original value. This illustrates the powerful effect that distance has on the interaction between charged particles.