Electric Field

Dielectric Constant and Electrostatic Force

We have two charges separated by a distance . In air, the force between them is . When placed in a dielectric medium at the same distance, the force becomes . We need to find the dielectric constant of the medium.

Step 1: Electrostatic Force in Air (Vacuum)

The electrostatic force between two charges and separated by a distance in a vacuum (or air, which is a good approximation) is given by Coulomb's Law:

Where:

• is the electrostatic force in air.
• is the permittivity of free space.
• and are the magnitudes of the charges.
• is the distance between the charges.

Step 2: Electrostatic Force in a Dielectric Medium

When the charges are placed in a dielectric medium, the electrostatic force is reduced by a factor of the dielectric constant . Let be the force in the dielectric medium:

Where is the dielectric constant (also known as the relative permittivity ).

Step 3: Relate the Forces

We are given that the force in the dielectric medium is :

Step 4: Solve for the Dielectric Constant

Substitute the expressions for and :

Notice that the terms appear on both sides, so we can cancel them out:

Solving for , we get:

Conclusion

The dielectric constant of the medium is 2.